Stochastic calculus for fractional Brownian motion and related processes:
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| Sprache: | English |
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Springer
2008
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| Schriftenreihe: | Lecture notes in mathematics
1929 |
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 393 S. |
| ISBN: | 9783540758723 3540758720 |
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| 100 | 1 | |a Mišura, Julija S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stochastic calculus for fractional Brownian motion and related processes |c Yuliya S. Mishura |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XVII, 393 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1929 | |
| 650 | 0 | 7 | |a Stochastische Analysis |0 (DE-588)4132272-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gebrochene Brownsche Bewegung |0 (DE-588)4780019-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Gebrochene Brownsche Bewegung |0 (DE-588)4780019-7 |D s |
| 689 | 0 | 1 | |a Stochastische Analysis |0 (DE-588)4132272-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Lecture notes in mathematics |v 1929 |w (DE-604)BV000676446 |9 1929 | |
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Datensatz im Suchindex
| _version_ | 1804137329854513152 |
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| adam_text | Contents
1 Wiener Integration
with Respect to Fractional Brownian
Motion
.................................................... 1
1.1
The Elements of Fractional Calculus
....................... 1
1.2
Fractional Brownian Motion: Definition and Elementary
Properties
.............................................. 7
1.3
Mandelbrot-van Ness Representation of fBm
................ 9
1.4
Fractional Brownian Motion with
H
€
(¿,
1)
on the White
Noise Space
............................................. 10
1.5
Fractional Noise on White Noise Space
..................... 12
1.6
Wiener Integration with Respect to fBm
................... 16
1.7
The Space of Gaussian Variables Generated by fBm
.......... 24
1.8
Representation of fBm via the Wiener Process on a Finite
Interval
................................................ 26
1.9
The Inequalities for the Moments of the Wiener Integrals
with Respect to fBm
..................................... 35
1.10
Maximal Inequalities for the Moments of Wiener Integrals
with Respect to fBm
..................................... 41
1.11
The Conditions of Continuity of Wiener Integrals with
Respect to fBm
......................................... 64
1.12
The Estimates of Moments of the Solution of Simple
Stochastic Differential Equations Involving fBm
............. 55
1.13
Stochastic Fubini Theorem for the Wiener Integrals
w.r.t fBm
............................................... 57
1.14
Martingale Transforms and Girsanov Theorem for Long-
memory Gaussian Processes
.............................. 58
1.15
Nonsemimartingale Properties of fBm; How to Approximate
Them by Semimartingales
................................ 71
1.15.1
Approximation of fflm by Continuous Processes of
Bounded Variation
................................ 71
1.15.2
Convergence
Вя^
->■
BH in
Besov
Space Wx[a,b]
..... 73
1.15.3
Weak Convergence to fBm in the Schemes of Series
.... 78
XIV Contents
1.16 Holder
Properties of the Trajectories of ffim and of Wiener
Integrals w.r.t. fBm
...................................... 87
1.17
Estimates for Fractional Derivatives of fBm and of Wiener
Integrals w.r.t. Wiener Process via the Garsia-Rodemich-
Rumsey Inequality
....................................... 88
1.18
Power Variations of fBm and of Wiener Integrals w.r.t. fBm
.. 90
1.19
Levy Theorem for fBm
................................... 94
1.20
Multi-parameter Fractional Brownian Motion
...............117
1.20.1
The Main Definition
...............................117
1.20.2
Holder Properties of Two-parameter fBm
.............117
1.20.3
Fractional Integrals and Fractional Derivatives of
Two-parameter Functions
..........................118
2
Stochastic Integration with Respect to fBm and Related
Topics
.....................................................123
2.1
Pathwise Stochastic Integration
...........................123
2.1.1
Pathwise Stochastic Integration in the Fractional
Sobolev-type Spaces
...............................123
2.1.2
Pathwise Stochastic Integration in Fractional
Besov-type Spaces
.................................128
2.2
Pathwise Stochastic Integration w.r.t. Multi-parameter fBm.
. . 131
2.2.1
Some Additional Properties of Two-parameter
Fractional Integrals and Derivatives
..................131
2.2.2
Generalized Two-parameter Lebesgue-Stieltjes
Integrals
.........................................132
2.2.3
Generalized Integrals of Two-parameter fBm in the
Case of the Integrand Depending on ffim
.............136
2.2.4
Pathwise Integration in Two-parameter
Besov
Spaces
.. 136
2.2.5
The Existence of the Integrals of the Second Kind of a
Two-parameter ffim
...............................137
2.3
Wick Integration with Respect to ffim with
Я Є
[1/2,1)
as
¿» -integration
...........................................141
2.3.1
Wick Products and ¿^-integration
...................141
2.3.2
Comparison of Wick and Pathwise Integrals for
Markov Integrands
..............................145
2.3.3
Comparison of Wick and Stratonovich Integrals for
General Integrands
..............................154
2.3.4
Reduction of Wick Integration w.r.t. Fractional Noise
to the Integration w.r.t. White Noise
.................157
2.4
Skorohod, Forward, Backward and Symmetric Integration
w.r.t. ffim. Two Approaches to Skorohod Integration
........158
2.5
Isometric Approach to Stochastic Integration with Respect
to ffim
.................................................162
2.5.1
The Basic Idea
....................................162
2.5.2
First- and Higher-order Integrals with Respect to X
... 164
2.5.3
Generalized Integrals with Respect to ffim
............169
Contents
XV
2.6
Stochastic
Pubini Theorem
for Stochastic
Integrals w.r.t.
Fractional
Brownian Motion..............................174
2.7 The
Ito Formula
for Fractional Brownian Motion
............182
2.7.1
The Simplest Version
..............................182
2.7.2
Ito
Formula for Linear Combination of Fractional
Brownian Motions with
Яг Є
[1/2,1)
in Terms of
Pathwise Integrals and
Ito
Integral
..................183
2.7.3
The
Ito
Formula in Terms of Wick Integrals
..........184
2.7.4
The
Ito
Formula for
Я Є
(0,1/2)....................185
2.7.5
Ito Formula
for Fractional Brownian Fields
...........186
2.7.6
The
Ito
Formula for
Я Є
(0,1)
in Terms of Isometric
Integrals, and Its Applications
......................189
2.8
The Girsanov Theorem for ffim and Its Applications
.........191
2.8.1
The Girsanov Theorem for fBm
.....................191
2.8.2
When the Conditions of the Girsanov Theorem Are
Fulfilled? Differentiability of the Fractional Integrals
... 193
Stochastic Differential Equations Involving Fractional
Brownian Motion
..........................................197
3.1
Stochastic Differential Equations Driven by Fractional
Brownian Motion with Pathwise Integrals
..................197
3.1.1
Existence and Uniqueness of Solutions: the Results of
Nualart and
Rancami
..............................197
3.1.2
Norm and Moment Estimates of Solution
.............202
3.1.3
Some Other Results on Existence and Uniqueness of
Solution of SDE Involving Processes Related to fBm
with
(Я є
(1/2,1))................................204
3.1.4
Some Properties of the Stochastic Differential
Equations with Stationary Coefficients
...............206
3.1.5 Semilinear
Stochastic Differential Equations Involving
Forward Integral w.r.t. fBm
.........................220
3.1.6
Existence and Uniqueness of Solutions of SDE with
Two-Parameter Fractional Brownian Field
............223
3.2
The Mixed SDE Involving Both the Wiener Process
and fBm
...............................................225
3.2.1
The Existence and Uniqueness of the Solution of the
Mixed
Semilinear SDE.............................225
3.2.2
The Existence and Uniqueness of the Solution of the
Mixed SDE for fBm with
Я є
(3/4,1) ...............227
3.2.3
The Girsanov Theorem and the Measure
Transformation for the Mixed
Semilinear SDE........238
3.3
Stochastic Differential Equations with Fractional
White Noise
............................................240
3.3.1
The Lipschitz and the Growth Conditions on the
Negative Norms of Coefficients
......................240
3.3.2 Quasilinear
SDE with Fractional Noise
...............241
XVI Contents
3.4
The Rate of Convergence of
Euler
Approximations of
Solutions of SDE Involving fBm
...........................243
3.4.1
Approximation of Pathwise Equations
................244
3.4.2
Approximation of
Quasilinear Skorohod-type
Equations
........................................255
3.5
SDE with the Additive Wiener Integral w.r.t. Fractional
Noise
..................................................262
3.5.1
Existence of a Weak Solution for Regular Coefficients
.. 263
3.5.2
Existence of a Weak Solution for SDE with
Discontinuous Drift
................................266
3.5.3
Uniqueness in Law and Pathwise Uniqueness for
Regular Coefficients
...............................271
3.5.4
Existence of a Strong Solution for the Regular Case.
... 272
3.5.5
Existence of a Strong Solution
for Discontinuous Drift
.............................274
3.5.6
Estimates of Moments of Solutions for Regular Case
and
Я Є
(0,1/2) ..................................278
3.5.7
The Estimates of the Norms of the Solution in the
Orlicz Spaces
.....................................280
3.5.8
The Distribution of the Supremum of the Process X
on [0,T]
..........................................284
3.5.9
Modulus of Continuity of Solution of Equation
Involving Fractional Brownian Motion
...............287
4
Filtering in Systems with Fractional Brownian Noise
......291
4.1
Optimal Filtering of a Mixed Brownian-Fractional-Brownian
Model with Fractional Brownian Observation Noise
..........291
4.2
Optimal Filtering in Conditionally Gaussian Linear Systems
with Mixed Signal and Fractional Brownian Observation
Noise
..................................................295
4.3
Optimal Filtering in Systems with Polynomial Fractional
Brownian Noise
.........................................298
5
Financial Applications of Fractional Brownian Motion
.....301
5.1
Discussion of the Arbitrage Problem
.......................301
5.1.1
Long-range Dependence in Economics and Finance
.... 301
5.1.2
Arbitrage in Pure Fractional Brownian Model.
The Original Rogers Approach
......................302
5.1.3
Arbitrage in the Pure Fractional Model.
Results of Shiryaev and Dasgupta
...................304
5.1.4
Mixed Brownian-Fractional-Brownian Model:
Absence of Arbitrage and Related Topics
.............305
5.1.5
Equilibrium of Financial Market. The Fractional
Burgers Equation
.................................321
5.2
The Different Forms of the Biack-Scholes Equation
..........322
5.2.1
The Black-Scholes Equation for the Mixed
Brownian-Fractional-Brownian Model
................322
Contents XVII
5.2.2
Discussion
of the Place of Wick Products and Wick-
Itô-Skorohod
Integral in the Problems of Arbitrage
and Replication in the Fractional Black-Scholes
Pricing Model
.....................................323
6
Statistical Inference with Fractional Brownian Motion
.....327
6.1
Testing Problems for the Density Process for fBm with
Different Drifts
..........................................327
6.1.1
Observations Based on the Whole Trajectory with
σ
and
Η
Known
....................................329
6.1.2
Discretely Observed Trajectory and
σ
Unknown
.......331
6.2
Goodness-of-fit Test
.....................................335
6.2.1
Introduction
......................................335
6.2.2
The Whole Trajectory Is Observed and the Parameters
μ
and
σ
Are Known
...............................335
6.2.3
Goodness-of-fit Tests with Discrete Observations
......337
6.2.4
On Volatility Estimation
...........................340
6.2.5
Goodness-of-fit Test with Unknown
μ
and
σ
..........342
6.3
Parameter Estimates in the Models Involving fBm
..........343
6.3.1
Consistency of the Drift Parameter Estimates in the
Pure Fractional Brownian Diffusion Model
............344
6.3.2
Consistency of the Drift Parameter Estimates in the
Mixed Brownian—fractional-Brownian Diffusion Model
with Linearly Dependent Wt and
B f
..............349
6.3.3
The Properties of Maximum Likelihood Estimates
in Diffusion Brownian-Fractional-Brownian Models
with Independent Components
......................354
A Mandelbrot—van Ness Representation: Some Related
Calculations
...............................................363
В
Approximation of Beta Integrals and Estimation
of Kernels
.................................................365
References
.....................................................369
Index
..........................................................391
|
| adam_txt |
Contents
1 Wiener Integration
with Respect to Fractional Brownian
Motion
. 1
1.1
The Elements of Fractional Calculus
. 1
1.2
Fractional Brownian Motion: Definition and Elementary
Properties
. 7
1.3
Mandelbrot-van Ness Representation of fBm
. 9
1.4
Fractional Brownian Motion with
H
€
(¿,
1)
on the White
Noise Space
. 10
1.5
Fractional Noise on White Noise Space
. 12
1.6
Wiener Integration with Respect to fBm
. 16
1.7
The Space of Gaussian Variables Generated by fBm
. 24
1.8
Representation of fBm via the Wiener Process on a Finite
Interval
. 26
1.9
The Inequalities for the Moments of the Wiener Integrals
with Respect to fBm
. 35
1.10
Maximal Inequalities for the Moments of Wiener Integrals
with Respect to fBm
. 41
1.11
The Conditions of Continuity of Wiener Integrals with
Respect to fBm
. 64
1.12
The Estimates of Moments of the Solution of Simple
Stochastic Differential Equations Involving fBm
. 55
1.13
Stochastic Fubini Theorem for the Wiener Integrals
w.r.t fBm
. 57
1.14
Martingale Transforms and Girsanov Theorem for Long-
memory Gaussian Processes
. 58
1.15
Nonsemimartingale Properties of fBm; How to Approximate
Them by Semimartingales
. 71
1.15.1
Approximation of fflm by Continuous Processes of
Bounded Variation
. 71
1.15.2
Convergence
Вя^
->■
BH in
Besov
Space Wx[a,b]
. 73
1.15.3
Weak Convergence to fBm in the Schemes of Series
. 78
XIV Contents
1.16 Holder
Properties of the Trajectories of ffim and of Wiener
Integrals w.r.t. fBm
. 87
1.17
Estimates for Fractional Derivatives of fBm and of Wiener
Integrals w.r.t. Wiener Process via the Garsia-Rodemich-
Rumsey Inequality
. 88
1.18
Power Variations of fBm and of Wiener Integrals w.r.t. fBm
. 90
1.19
Levy Theorem for fBm
. 94
1.20
Multi-parameter Fractional Brownian Motion
.117
1.20.1
The Main Definition
.117
1.20.2
Holder Properties of Two-parameter fBm
.117
1.20.3
Fractional Integrals and Fractional Derivatives of
Two-parameter Functions
.118
2
Stochastic Integration with Respect to fBm and Related
Topics
.123
2.1
Pathwise Stochastic Integration
.123
2.1.1
Pathwise Stochastic Integration in the Fractional
Sobolev-type Spaces
.123
2.1.2
Pathwise Stochastic Integration in Fractional
Besov-type Spaces
.128
2.2
Pathwise Stochastic Integration w.r.t. Multi-parameter fBm.
. . 131
2.2.1
Some Additional Properties of Two-parameter
Fractional Integrals and Derivatives
.131
2.2.2
Generalized Two-parameter Lebesgue-Stieltjes
Integrals
.132
2.2.3
Generalized Integrals of Two-parameter fBm in the
Case of the Integrand Depending on ffim
.136
2.2.4
Pathwise Integration in Two-parameter
Besov
Spaces
. 136
2.2.5
The Existence of the Integrals of the Second Kind of a
Two-parameter ffim
.137
2.3
Wick Integration with Respect to ffim with
Я Є
[1/2,1)
as
¿»"-integration
.141
2.3.1
Wick Products and ¿^-integration
.141
2.3.2
Comparison of Wick and Pathwise Integrals for
"Markov" Integrands
.145
2.3.3
Comparison of Wick and Stratonovich Integrals for
"General" Integrands
.154
2.3.4
Reduction of Wick Integration w.r.t. Fractional Noise
to the Integration w.r.t. White Noise
.157
2.4
Skorohod, Forward, Backward and Symmetric Integration
w.r.t. ffim. Two Approaches to Skorohod Integration
.158
2.5
Isometric Approach to Stochastic Integration with Respect
to ffim
.162
2.5.1
The Basic Idea
.162
2.5.2
First- and Higher-order Integrals with Respect to X
. 164
2.5.3
Generalized Integrals with Respect to ffim
.169
Contents
XV
2.6
Stochastic
Pubini Theorem
for Stochastic
Integrals w.r.t.
Fractional
Brownian Motion.174
2.7 The
Ito Formula
for Fractional Brownian Motion
.182
2.7.1
The Simplest Version
.182
2.7.2
Ito
Formula for Linear Combination of Fractional
Brownian Motions with
Яг Є
[1/2,1)
in Terms of
Pathwise Integrals and
Ito
Integral
.183
2.7.3
The
Ito
Formula in Terms of Wick Integrals
.184
2.7.4
The
Ito
Formula for
Я Є
(0,1/2).185
2.7.5
Ito Formula
for Fractional Brownian Fields
.186
2.7.6
The
Ito
Formula for
Я Є
(0,1)
in Terms of Isometric
Integrals, and Its Applications
.189
2.8
The Girsanov Theorem for ffim and Its Applications
.191
2.8.1
The Girsanov Theorem for fBm
.191
2.8.2
When the Conditions of the Girsanov Theorem Are
Fulfilled? Differentiability of the Fractional Integrals
. 193
Stochastic Differential Equations Involving Fractional
Brownian Motion
.197
3.1
Stochastic Differential Equations Driven by Fractional
Brownian Motion with Pathwise Integrals
.197
3.1.1
Existence and Uniqueness of Solutions: the Results of
Nualart and
Rancami
.197
3.1.2
Norm and Moment Estimates of Solution
.202
3.1.3
Some Other Results on Existence and Uniqueness of
Solution of SDE Involving Processes Related to fBm
with
(Я є
(1/2,1)).204
3.1.4
Some Properties of the Stochastic Differential
Equations with Stationary Coefficients
.206
3.1.5 Semilinear
Stochastic Differential Equations Involving
Forward Integral w.r.t. fBm
.220
3.1.6
Existence and Uniqueness of Solutions of SDE with
Two-Parameter Fractional Brownian Field
.223
3.2
The Mixed SDE Involving Both the Wiener Process
and fBm
.225
3.2.1
The Existence and Uniqueness of the Solution of the
Mixed
Semilinear SDE.225
3.2.2
The Existence and Uniqueness of the Solution of the
Mixed SDE for fBm with
Я є
(3/4,1) .227
3.2.3
The Girsanov Theorem and the Measure
Transformation for the Mixed
Semilinear SDE.238
3.3
Stochastic Differential Equations with Fractional
White Noise
.240
3.3.1
The Lipschitz and the Growth Conditions on the
Negative Norms of Coefficients
.240
3.3.2 Quasilinear
SDE with Fractional Noise
.241
XVI Contents
3.4
The Rate of Convergence of
Euler
Approximations of
Solutions of SDE Involving fBm
.243
3.4.1
Approximation of Pathwise Equations
.244
3.4.2
Approximation of
Quasilinear Skorohod-type
Equations
.255
3.5
SDE with the Additive Wiener Integral w.r.t. Fractional
Noise
.262
3.5.1
Existence of a Weak Solution for Regular Coefficients
. 263
3.5.2
Existence of a Weak Solution for SDE with
Discontinuous Drift
.266
3.5.3
Uniqueness in Law and Pathwise Uniqueness for
Regular Coefficients
.271
3.5.4
Existence of a Strong Solution for the Regular Case.
. 272
3.5.5
Existence of a Strong Solution
for Discontinuous Drift
.274
3.5.6
Estimates of Moments of Solutions for Regular Case
and
Я Є
(0,1/2) .278
3.5.7
The Estimates of the Norms of the Solution in the
Orlicz Spaces
.280
3.5.8
The Distribution of the Supremum of the Process X
on [0,T]
.284
3.5.9
Modulus of Continuity of Solution of Equation
Involving Fractional Brownian Motion
.287
4
Filtering in Systems with Fractional Brownian Noise
.291
4.1
Optimal Filtering of a Mixed Brownian-Fractional-Brownian
Model with Fractional Brownian Observation Noise
.291
4.2
Optimal Filtering in Conditionally Gaussian Linear Systems
with Mixed Signal and Fractional Brownian Observation
Noise
.295
4.3
Optimal Filtering in Systems with Polynomial Fractional
Brownian Noise
.298
5
Financial Applications of Fractional Brownian Motion
.301
5.1
Discussion of the Arbitrage Problem
.301
5.1.1
Long-range Dependence in Economics and Finance
. 301
5.1.2
Arbitrage in "Pure" Fractional Brownian Model.
The Original Rogers Approach
.302
5.1.3
Arbitrage in the "Pure" Fractional Model.
Results of Shiryaev and Dasgupta
.304
5.1.4
Mixed Brownian-Fractional-Brownian Model:
Absence of Arbitrage and Related Topics
.305
5.1.5
Equilibrium of Financial Market. The Fractional
Burgers Equation
.321
5.2
The Different Forms of the Biack-Scholes Equation
.322
5.2.1
The Black-Scholes Equation for the Mixed
Brownian-Fractional-Brownian Model
.322
Contents XVII
5.2.2
Discussion
of the Place of Wick Products and Wick-
Itô-Skorohod
Integral in the Problems of Arbitrage
and Replication in the Fractional Black-Scholes
Pricing Model
.323
6
Statistical Inference with Fractional Brownian Motion
.327
6.1
Testing Problems for the Density Process for fBm with
Different Drifts
.327
6.1.1
Observations Based on the Whole Trajectory with
σ
and
Η
Known
.329
6.1.2
Discretely Observed Trajectory and
σ
Unknown
.331
6.2
Goodness-of-fit Test
.335
6.2.1
Introduction
.335
6.2.2
The Whole Trajectory Is Observed and the Parameters
μ
and
σ
Are Known
.335
6.2.3
Goodness-of-fit Tests with Discrete Observations
.337
6.2.4
On Volatility Estimation
.340
6.2.5
Goodness-of-fit Test with Unknown
μ
and
σ
.342
6.3
Parameter Estimates in the Models Involving fBm
.343
6.3.1
Consistency of the Drift Parameter Estimates in the
Pure Fractional Brownian Diffusion Model
.344
6.3.2
Consistency of the Drift Parameter Estimates in the
Mixed Brownian—fractional-Brownian Diffusion Model
with "Linearly" Dependent Wt and
B f
.349
6.3.3
The Properties of Maximum Likelihood Estimates
in Diffusion Brownian-Fractional-Brownian Models
with Independent Components
.354
A Mandelbrot—van Ness Representation: Some Related
Calculations
.363
В
Approximation of Beta Integrals and Estimation
of Kernels
.365
References
.369
Index
.391 |
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| author | Mišura, Julija S. |
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| dewey-search | 510 519.233 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV023081406 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:37:18Z |
| indexdate | 2024-07-09T21:10:34Z |
| institution | BVB |
| isbn | 9783540758723 3540758720 |
| language | English |
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| oclc_num | 441598787 |
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| physical | XVII, 393 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Mišura, Julija S. Verfasser aut Stochastic calculus for fractional Brownian motion and related processes Yuliya S. Mishura Berlin [u.a.] Springer 2008 XVII, 393 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1929 Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Gebrochene Brownsche Bewegung (DE-588)4780019-7 gnd rswk-swf Gebrochene Brownsche Bewegung (DE-588)4780019-7 s Stochastische Analysis (DE-588)4132272-1 s DE-604 Lecture notes in mathematics 1929 (DE-604)BV000676446 1929 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016284423&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mišura, Julija S. Stochastic calculus for fractional Brownian motion and related processes Lecture notes in mathematics Stochastische Analysis (DE-588)4132272-1 gnd Gebrochene Brownsche Bewegung (DE-588)4780019-7 gnd |
| subject_GND | (DE-588)4132272-1 (DE-588)4780019-7 |
| title | Stochastic calculus for fractional Brownian motion and related processes |
| title_auth | Stochastic calculus for fractional Brownian motion and related processes |
| title_exact_search | Stochastic calculus for fractional Brownian motion and related processes |
| title_exact_search_txtP | Stochastic calculus for fractional Brownian motion and related processes |
| title_full | Stochastic calculus for fractional Brownian motion and related processes Yuliya S. Mishura |
| title_fullStr | Stochastic calculus for fractional Brownian motion and related processes Yuliya S. Mishura |
| title_full_unstemmed | Stochastic calculus for fractional Brownian motion and related processes Yuliya S. Mishura |
| title_short | Stochastic calculus for fractional Brownian motion and related processes |
| title_sort | stochastic calculus for fractional brownian motion and related processes |
| topic | Stochastische Analysis (DE-588)4132272-1 gnd Gebrochene Brownsche Bewegung (DE-588)4780019-7 gnd |
| topic_facet | Stochastische Analysis Gebrochene Brownsche Bewegung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016284423&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT misurajulijas stochasticcalculusforfractionalbrownianmotionandrelatedprocesses |