Introduction to stochastic calculus with applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Imperial College Press
2005
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Table of contents Inhaltsverzeichnis |
| Physical Description: | XIII, 416 S. graph. Darst. |
| ISBN: | 186094566X 1860945554 |
Staff View
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| 245 | 1 | 0 | |a Introduction to stochastic calculus with applications |c Fima C. Klebaner |
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| adam_text | FIMA C KLEBANER MONASH UNIVERSITY, AUSTRALIA ICP IMPERIAL COLLEGE PRESS
CONTENTS PREFACE V 1 PRELIMINARIES FROM CALCULUS 1 1.1 FUNCTIONS IN
CALCULUS 1 1.2 VARIATION OF A FUNCTION 4 1.3 RIEMANN INTEGRAL AND
STIELTJES INTEGRAL 9 1.4 LEBESGUE S METHOD OF INTEGRATION 14 1.5
DIFFERENTIALS AND INTEGRALS 14 1.6 TAYLOR S FORMULA AND OTHER RESULTS 15
2 CONCEPTS OF PROBABILITY THEORY 21 2.1 DISCRETE PROBABILITY MODEL 21
2.2 CONTINUOUS PROBABILITY MODEL 28 2.3 EXPECTATION AND LEBESGUE
INTEGRAL 33 2.4 TRANSFORMS AND CONVERGENCE 37 2.5 INDEPENDENCE AND
COVARIANCE 39 2.6 NORMAL (GAUSSIAN) DISTRIBUTIONS 41 2.7 CONDITIONAL
EXPECTATION 43 2.8 STOCHASTIC PROCESSES IN CONTINUOUS TIME 47 3 BASIC
STOCHASTIC PROCESSES 55 3.1 BROWNIAN MOTION 56 3.2 PROPERTIES OF
BROWNIAN MOTION PATHS 63 3.3 THREE MARTINGALES OF BROWNIAN MOTION 65 3.4
MARKOV PROPERTY OF BROWNIAN MOTION . 67 3.5 HITTING TIMES AND EXIT TIMES
69 3.6 MAXIMUM AND MINIMUM OF BROWNIAN MOTION 71 3.7 DISTRIBUTION OF
HITTING TIMES 73 3.8 REFLECTION PRINCIPLE AND JOINT DISTRIBUTIONS 74 3.9
ZEROS OF BROWNIAN MOTION. ARCSINE LAW 75 IX PREFACE 3.10 SIZE OF
INCREMENTS OF BROWNIAN MOTION 78 3.11 BROWNIAN MOTION IN HIGHER
DIMENSIONS 81 3.12 RANDOM WALK 81 3.13 STOCHASTIC INTEGRAL IN DISCRETE
TIME 83 3.14 POISSON PROCESS 86 3.15 EXERCISES 88 BROWNIAN MOTION
CALCULUS 91 4.1 DEFINITION DF ITO INTEGRAL 91 4.2 ITO INTEGRAL PROCESS
100 4.3 ITO INTEGRAL AND GAUSSIAN PROCESSES 103 4.4 ITO S FORMULA FOR
BROWNIAN MOTION 105 4.5 ITO PROCESSES AND STOCHASTIC DIFFERENTIALS 108
4.6 ITO S FORMULA FOR ITO PROCESSES ILL 4.7 ITO PROCESSES IN HIGHER
DIMENSIONS 117 4.8 EXERCISES 120 STOCHASTIC DIFFERENTIAL EQUATIONS 123
5.1 DEFINITION OF STOCHASTIC DIFFERENTIAL EQUATIONS 123 5.2 STOCHASTIC
EXPONENTIAL AND LOGARITHM 128 5.3 SOLUTIONS TO LINEAR SDES 130 5.4
EXISTENCE AND UNIQUENESS OF STRONG SOLUTIONS 133 5.5 MARKOV PROPERTY OF
SOLUTIONS 135 5.6 WEAK SOLUTIONS TO SDES 136 5.7 CONSTRUCTION OF WEAK
SOLUTIONS 138 5.8 BACKWARD AND FORWARD EQUATIONS 143 5.9 STRATANOVICH
STOCHASTIC CALCULUS 145 5.10 EXERCISES 147 DIFFUSION PROCESSES 149 6.1
MARTINGALES AND DYNKIN S FORMULA 149 6.2 CALCULATION OF EXPECTATIONS AND
PDES 153 6.3 TIME HOMOGENEOUS DIFFUSIONS 156 6.4 EXIT TIMES FROM AN
INTERVAL 160 6.5 REPRESENTATION OF SOLUTIONS OF ODES 165 6.6 EXPLOSION
166 6.7 RECURRENCE AND TRANSIENCE 167 6.8 DIFFUSION ON AN INTERVAL 169
6.9 STATIONARY DISTRIBUTIONS 170 6.10 MULTI-DIMENSIONAL SDES 173 6.11
EXERCISES 180 PREFACE XI 7 MARTINGALES 183 7.1 DEFINITIONS 183 7.2
UNIFORM INTEGRABILITY 185 7.3 MARTINGALE CONVERGENCE 187 7.4 OPTIONAL
STOPPING 189 7.5 LOCALIZATION AND LOCAL MARTINGALES 195 7.6 QUADRATIC
VARIATION OF MARTINGALES 198 7.7 MARTINGALE INEQUALITIES 200 7.8
CONTINUOUS MARTINGALES. CHANGE OF TIME 202 7.9 EXERCISES 209 8 CALCULUS
FOR SEMIMARTINGALES 211 8.1 SEMIMARTINGALES 211 8.2 PREDICTABLE
PROCESSES 212 8.3 DOOB-MEYER DECOMPOSITION 214 8.4 INTEGRALS WITH
RESPECT TO SEMIMARTINGALES 215 8.5 QUADRATIC VARIATION AND COVARIATION
218 8.6 ITO S FORMULA FOR CONTINUOUS SEMIMARTINGALES 220 8.7 LOCAL TIMES
222 8.8 STOCHASTIC EXPONENTIAL 224 8.9 COMPENSATORS AND SHARP BRACKET
PROCESS 228 8.10 ITO S FORMULA FOR SEMIMARTINGALES 234 8.11 STOCHASTIC
EXPONENTIAL AND LOGARITHM 236 8.12 MARTINGALE (PREDICTABLE)
REPRESENTATIONS 237 8.13 ELEMENTS OF THE GENERAL THEORY 240 8.14 RANDOM
MEASURES AND CANONICAL DECOMPOSITION 244 8.15 EXERCISES 247 9 PURE JUMP
PROCESSES 249 9.1 DEFINITIONS 249 9.2 PURE JUMP PROCESS FILTRATION 250
9.3 ITO S FORMULA FOR PROCESSES OF FINITE VARIATION 251 9.4 COUNTING
PROCESSES 252 9.5 MARKOV JUMP PROCESSES 259 9.6 STOCHASTIC EQUATION FOR
JUMP PROCESSES 261 9.7 EXPLOSIONS IN MARKOV JUMP PROCESSES 263 9.8
EXERCISES 265 XII PREFACE 10 CHANGE OF PROBABILITY MEASURE 267 10.1
CHANGE OF MEASURE FOR RANDOM VARIABLES 267 10.2 CHANGE OF MEASURE ON A
GENERAL SPACE 271 10.3 CHANGE OF MEASURE FOR PROCESSES 274 10.4 CHANGE
OF WIENER MEASURE 279 10.5 CHANGE OF MEASURE FOR POINT PROCESSES 280
10.6 LIKELIHOOD FUNCTIONS 282 10.7 EXERCISES V 285 11 APPLICATIONS IN
FINANCE: STOCK AND FX OPTIONS 287 11.1 FINANCIAL DERIVATIVES AND
ARBITRAGE 287 11.2 A FINITE MARKET MODEL 293 11.3 SEMIMARTINGALE MARKET
MODEL 297 11.4 DIFFUSION AND THE BLACK-SCHOLES MODEL 302 11.5 CHANGE OF
NUMERAIRE 310 11.6 CURRENCY (FX) OPTIONS 312 11.7 ASIAN, LOOKBACK AND
BARRIER OPTIONS 315 11.8 EXERCISES 319 12 APPLICATIONS IN FINANCE:
BONDS, RATES AND OPTIONS 323 12.1 BONDS AND THE YIELD CURVE 323 12.2
MODELS ADAPTED TO BROWNIAN MOTION 325 12.3 MODELS BASED ON THE SPOT RATE
326 12.4 MERTON S MODEL AND VASICEK S MODEL 327 12.5 HEATH-JARROW-MORTON
(HJM) MODEL 331 12.6 FORWARD MEASURES. BOND AS A NUMERAIRE 336 12.7
OPTIONS, CAPS AND FLOORS 339 12.8 BRACE-GATAREK-MUSIELA (BGM) MODEL 341
12.9 SWAPS AND SWAPTIONS 345 12.10 EXERCISES 347 13 APPLICATIONS IN
BIOLOGY 351 13.1 FELLER S BRANCHING DIFFUSION 351 13.2 WRIGHT-FISHER
DIFFUSION 354 13.3 BIRTH-DEATH PROCESSES 356 13.4 BRANCHING PROCESSES
360 13.5 STOCHASTIC LOTKA-VOLTERRA MODEL 366 13.6 EXERCISES 373 PREFACE
XIII 14 APPLICATIONS IN ENGINEERING AND PHYSICS 375 14.1 FILTERING 375
14.2 RANDOM OSCILLATORS 382 14.3 EXERCISES 388 SOLUTIONS TO SELECTED
EXERCISES 391 REFERENCES 407 INDEX 413
|
| adam_txt |
FIMA C KLEBANER MONASH UNIVERSITY, AUSTRALIA ICP IMPERIAL COLLEGE PRESS
CONTENTS PREFACE V 1 PRELIMINARIES FROM CALCULUS 1 1.1 FUNCTIONS IN
CALCULUS 1 1.2 VARIATION OF A FUNCTION 4 1.3 RIEMANN INTEGRAL AND
STIELTJES INTEGRAL 9 1.4 LEBESGUE'S METHOD OF INTEGRATION 14 1.5
DIFFERENTIALS AND INTEGRALS 14 1.6 TAYLOR'S FORMULA AND OTHER RESULTS 15
2 CONCEPTS OF PROBABILITY THEORY 21 2.1 DISCRETE PROBABILITY MODEL 21
2.2 CONTINUOUS PROBABILITY MODEL 28 2.3 EXPECTATION AND LEBESGUE
INTEGRAL 33 2.4 TRANSFORMS AND CONVERGENCE 37 2.5 INDEPENDENCE AND
COVARIANCE 39 2.6 NORMAL (GAUSSIAN) DISTRIBUTIONS 41 2.7 CONDITIONAL
EXPECTATION 43 2.8 STOCHASTIC PROCESSES IN CONTINUOUS TIME 47 3 BASIC
STOCHASTIC PROCESSES 55 3.1 BROWNIAN MOTION 56 3.2 PROPERTIES OF
BROWNIAN MOTION PATHS 63 3.3 THREE MARTINGALES OF BROWNIAN MOTION 65 3.4
MARKOV PROPERTY OF BROWNIAN MOTION . 67 3.5 HITTING TIMES AND EXIT TIMES
69 3.6 MAXIMUM AND MINIMUM OF BROWNIAN MOTION 71 3.7 DISTRIBUTION OF
HITTING TIMES 73 3.8 REFLECTION PRINCIPLE AND JOINT DISTRIBUTIONS 74 3.9
ZEROS OF BROWNIAN MOTION. ARCSINE LAW 75 IX PREFACE 3.10 SIZE OF
INCREMENTS OF BROWNIAN MOTION 78 3.11 BROWNIAN MOTION IN HIGHER
DIMENSIONS 81 3.12 RANDOM WALK 81 3.13 STOCHASTIC INTEGRAL IN DISCRETE
TIME 83 3.14 POISSON PROCESS 86 3.15 EXERCISES 88 BROWNIAN MOTION
CALCULUS 91 4.1 DEFINITION DF ITO INTEGRAL 91 4.2 ITO INTEGRAL PROCESS
100 4.3 ITO INTEGRAL AND GAUSSIAN PROCESSES 103 4.4 ITO'S FORMULA FOR
BROWNIAN MOTION 105 4.5 ITO PROCESSES AND STOCHASTIC DIFFERENTIALS 108
4.6 ITO'S FORMULA FOR ITO PROCESSES ILL 4.7 ITO PROCESSES IN HIGHER
DIMENSIONS 117 4.8 EXERCISES 120 STOCHASTIC DIFFERENTIAL EQUATIONS 123
5.1 DEFINITION OF STOCHASTIC DIFFERENTIAL EQUATIONS 123 5.2 STOCHASTIC
EXPONENTIAL AND LOGARITHM 128 5.3 SOLUTIONS TO LINEAR SDES 130 5.4
EXISTENCE AND UNIQUENESS OF STRONG SOLUTIONS 133 5.5 MARKOV PROPERTY OF
SOLUTIONS 135 5.6 WEAK SOLUTIONS TO SDES 136 5.7 CONSTRUCTION OF WEAK
SOLUTIONS 138 5.8 BACKWARD AND FORWARD EQUATIONS 143 5.9 STRATANOVICH
STOCHASTIC CALCULUS 145 5.10 EXERCISES 147 DIFFUSION PROCESSES 149 6.1
MARTINGALES AND DYNKIN'S FORMULA 149 6.2 CALCULATION OF EXPECTATIONS AND
PDES 153 6.3 TIME HOMOGENEOUS DIFFUSIONS 156 6.4 EXIT TIMES FROM AN
INTERVAL 160 6.5 REPRESENTATION OF SOLUTIONS OF ODES 165 6.6 EXPLOSION
166 6.7 RECURRENCE AND TRANSIENCE 167 6.8 DIFFUSION ON AN INTERVAL 169
6.9 STATIONARY DISTRIBUTIONS 170 6.10 MULTI-DIMENSIONAL SDES 173 6.11
EXERCISES 180 PREFACE XI 7 MARTINGALES 183 7.1 DEFINITIONS 183 7.2
UNIFORM INTEGRABILITY 185 7.3 MARTINGALE CONVERGENCE 187 7.4 OPTIONAL
STOPPING 189 7.5 LOCALIZATION AND LOCAL MARTINGALES 195 7.6 QUADRATIC
VARIATION OF MARTINGALES 198 7.7 MARTINGALE INEQUALITIES 200 7.8
CONTINUOUS MARTINGALES. CHANGE OF TIME 202 7.9 EXERCISES 209 8 CALCULUS
FOR SEMIMARTINGALES 211 8.1 SEMIMARTINGALES 211 8.2 PREDICTABLE
PROCESSES 212 8.3 DOOB-MEYER DECOMPOSITION 214 8.4 INTEGRALS WITH
RESPECT TO SEMIMARTINGALES 215 8.5 QUADRATIC VARIATION AND COVARIATION
218 8.6 ITO'S FORMULA FOR CONTINUOUS SEMIMARTINGALES 220 8.7 LOCAL TIMES
222 8.8 STOCHASTIC EXPONENTIAL 224 8.9 COMPENSATORS AND SHARP BRACKET
PROCESS 228 8.10 ITO'S FORMULA FOR SEMIMARTINGALES 234 8.11 STOCHASTIC
EXPONENTIAL AND LOGARITHM 236 8.12 MARTINGALE (PREDICTABLE)
REPRESENTATIONS 237 8.13 ELEMENTS OF THE GENERAL THEORY 240 8.14 RANDOM
MEASURES AND CANONICAL DECOMPOSITION 244 8.15 EXERCISES 247 9 PURE JUMP
PROCESSES 249 9.1 DEFINITIONS 249 9.2 PURE JUMP PROCESS FILTRATION 250
9.3 ITO'S FORMULA FOR PROCESSES OF FINITE VARIATION 251 9.4 COUNTING
PROCESSES 252 9.5 MARKOV JUMP PROCESSES 259 9.6 STOCHASTIC EQUATION FOR
JUMP PROCESSES 261 9.7 EXPLOSIONS IN MARKOV JUMP PROCESSES 263 9.8
EXERCISES 265 XII PREFACE 10 CHANGE OF PROBABILITY MEASURE 267 10.1
CHANGE OF MEASURE FOR RANDOM VARIABLES 267 10.2 CHANGE OF MEASURE ON A
GENERAL SPACE 271 10.3 CHANGE OF MEASURE FOR PROCESSES 274 10.4 CHANGE
OF WIENER MEASURE 279 10.5 CHANGE OF MEASURE FOR POINT PROCESSES 280
10.6 LIKELIHOOD FUNCTIONS 282 10.7 EXERCISES V 285 11 APPLICATIONS IN
FINANCE: STOCK AND FX OPTIONS 287 11.1 FINANCIAL DERIVATIVES AND
ARBITRAGE 287 11.2 A FINITE MARKET MODEL 293 11.3 SEMIMARTINGALE MARKET
MODEL 297 11.4 DIFFUSION AND THE BLACK-SCHOLES MODEL 302 11.5 CHANGE OF
NUMERAIRE 310 11.6 CURRENCY (FX) OPTIONS 312 11.7 ASIAN, LOOKBACK AND
BARRIER OPTIONS 315 11.8 EXERCISES 319 12 APPLICATIONS IN FINANCE:
BONDS, RATES AND OPTIONS 323 12.1 BONDS AND THE YIELD CURVE 323 12.2
MODELS ADAPTED TO BROWNIAN MOTION 325 12.3 MODELS BASED ON THE SPOT RATE
326 12.4 MERTON'S MODEL AND VASICEK'S MODEL 327 12.5 HEATH-JARROW-MORTON
(HJM) MODEL 331 12.6 FORWARD MEASURES. BOND AS A NUMERAIRE 336 12.7
OPTIONS, CAPS AND FLOORS 339 12.8 BRACE-GATAREK-MUSIELA (BGM) MODEL 341
12.9 SWAPS AND SWAPTIONS 345 12.10 EXERCISES 347 13 APPLICATIONS IN
BIOLOGY 351 13.1 FELLER'S BRANCHING DIFFUSION 351 13.2 WRIGHT-FISHER
DIFFUSION 354 13.3 BIRTH-DEATH PROCESSES 356 13.4 BRANCHING PROCESSES
360 13.5 STOCHASTIC LOTKA-VOLTERRA MODEL 366 13.6 EXERCISES 373 PREFACE
XIII 14 APPLICATIONS IN ENGINEERING AND PHYSICS 375 14.1 FILTERING 375
14.2 RANDOM OSCILLATORS 382 14.3 EXERCISES 388 SOLUTIONS TO SELECTED
EXERCISES 391 REFERENCES 407 INDEX 413 |
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| ctrlnum | (OCoLC)61263806 (DE-599)BVBBV022189247 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
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| id | DE-604.BV022189247 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:03:12Z |
| indexdate | 2024-07-09T20:46:20Z |
| institution | BVB |
| isbn | 186094566X 1860945554 |
| language | English |
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| owner | DE-824 |
| owner_facet | DE-824 |
| physical | XIII, 416 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Imperial College Press |
| record_format | marc |
| spelling | Klebaner, Fima C. Verfasser (DE-588)173351743 aut Introduction to stochastic calculus with applications Fima C. Klebaner 2. ed. London [u.a.] Imperial College Press 2005 XIII, 416 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analyse stochastique Análise estocastica larpcal Calcul infinitésimal Finanças larpcal Processos estocasticos larpcal Stochastic analysis Calculus Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Stochastische Analysis (DE-588)4132272-1 s DE-604 Stochastisches Integral (DE-588)4126478-2 s 1\p DE-604 http://www.loc.gov/catdir/toc/fy0605/2006272433.html Table of contents HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015083220&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Klebaner, Fima C. Introduction to stochastic calculus with applications Analyse stochastique Análise estocastica larpcal Calcul infinitésimal Finanças larpcal Processos estocasticos larpcal Stochastic analysis Calculus Stochastische Analysis (DE-588)4132272-1 gnd Stochastisches Integral (DE-588)4126478-2 gnd |
| subject_GND | (DE-588)4132272-1 (DE-588)4126478-2 |
| title | Introduction to stochastic calculus with applications |
| title_auth | Introduction to stochastic calculus with applications |
| title_exact_search | Introduction to stochastic calculus with applications |
| title_exact_search_txtP | Introduction to stochastic calculus with applications |
| title_full | Introduction to stochastic calculus with applications Fima C. Klebaner |
| title_fullStr | Introduction to stochastic calculus with applications Fima C. Klebaner |
| title_full_unstemmed | Introduction to stochastic calculus with applications Fima C. Klebaner |
| title_short | Introduction to stochastic calculus with applications |
| title_sort | introduction to stochastic calculus with applications |
| topic | Analyse stochastique Análise estocastica larpcal Calcul infinitésimal Finanças larpcal Processos estocasticos larpcal Stochastic analysis Calculus Stochastische Analysis (DE-588)4132272-1 gnd Stochastisches Integral (DE-588)4126478-2 gnd |
| topic_facet | Analyse stochastique Análise estocastica Calcul infinitésimal Finanças Processos estocasticos Stochastic analysis Calculus Stochastische Analysis Stochastisches Integral |
| url | http://www.loc.gov/catdir/toc/fy0605/2006272433.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015083220&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT klebanerfimac introductiontostochasticcalculuswithapplications |