Parameter estimation in stochastic differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Series: | Lecture notes in mathematics
1923 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 264 S. 235 mm x 155 mm |
| ISBN: | 9783540744474 3540744479 |
Staff View
MARC
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| 100 | 1 | |a Bishwal, Jaya P. N. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Parameter estimation in stochastic differential equations |c Jaya P. N. Bishwal |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XI, 264 S. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1923 | |
| 650 | 7 | |a Equações diferenciais estocásticas |2 larpcal | |
| 650 | 4 | |a Estimation d'un paramètre | |
| 650 | 7 | |a Processos estocásticos |2 larpcal | |
| 650 | 4 | |a Équations différentielles stochastiques | |
| 650 | 4 | |a Parameter estimation | |
| 650 | 4 | |a Stochastic differential equations | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Basic Notations XIII
1 Parametric Stochastic Differential Equations 1
Part I Continuous Sampling
2 Rates of Weak Convergence of Estimators in Homogeneous
Diffusions 15
2.1 Introduction 15
2.2 Berry Esseen Bounds for Estimators in the Ornstein
Uhlenbeck Process 16
2.3 Rates of Convergence in the Bernstein von Mises Theorem
for Ergodic Diffusions 26
2.4 Rates of Convergence of the Posterior Distributions
in Ergodic Diffusions 33
2.5 Berry Esseen Bound for the Bayes Estimator 41
2.6 Example: Hyperbolic Diffusion Model 47
3 Large Deviations of Estimators in Homogeneous
Diffusions 49
3.1 Introduction 49
3.2 Model, Assumptions and Preliminaries 50
3.3 Large Deviations for the Maximum Likelihood Estimator 51
3.4 Large Deviations for Bayes Estimators 57
3.5 Examples 59
4 Local Asymptotic Mixed Normality for Nonhomogeneous
Diffusions 61
4.1 Introduction 61
4.2 Model, Assumptions and Preliminaries 63
X Contents
4.3 Asymptotics of the Maximum Likelihood Estimator 67
4.4 The Bernstein von Mises Type Theorem and Asymptotics
of Bayes Estimators 68
4.5 Asymptotics of Maximum Probability Estimator 74
4.6 Examples 75
5 Bayes and Sequential Estimation in Stochastic PDEs 79
5.1 Long Time Asymptotics 79
5.1.1 Introduction 79
5.1.2 Model, Assumptions and Preliminaries 80
5.1.3 Bernstein von Mises Theorem 82
5.1.4 Asymptotics of Bayes Estimators 84
5.2 Sequential Estimation 85
5.2.1 Sequential Maximum Likelihood Estimation 85
5.2.2 Example 87
5.3 Spectral Asymptotics 88
5.3.1 Introduction 88
5.3.2 Model and Preliminaries 90
5.3.3 The Bernstein von Mises Theorem 93
5.3.4 Bayes Estimation 95
5.3.5 Example: Stochastic Heat Equation 96
6 Maximum Likelihood Estimation in Fractional
Diffusions 99
6.1 Introduction 99
6.2 Fractional Stochastic Calculus 100
6.3 Maximum Likelihood Estimation in Directly Observed
Fractional Diffusions 109
6.4 Maximum Likelihood Estimation in Partially Observed
Fractional Diffusions 113
6.5 Examples 118
Part II Discrete Sampling
7 Approximate Maximum Likelihood Estimation
in Nonhomogeneous Diffusions 125
7.1 Introduction 125
7.2 Model, Assumptions and Definitions 127
7.3 Accuracy of Approximations of the ltd and FS Integrals 135
7.4 Accuracy of Approximations of the Log likelihood Function . . . 142
7.5 Accuracy of Approximations of the Maximum Likelihood
Estimate 146
7.6 Example: Chan Karloyi Longstaff Sanders Model 148
7.7 Summary of Truncated Distributions 155
Contents XI
8 Rates of Weak Convergence of Estimators
in the Ornstein Uhlenbeck Process 159
8.1 Introduction 159
8.2 Notations and Preliminaries 160
8.3 Berry Esseen Type Bounds for AMLE1 162
8.4 Berry Esseen Type Bounds for AMLE2 173
8.5 Berry Esseen Type Bounds for Approximate Minimum
Contrast Estimators 178
8.6 Berry Esseen Bounds for Approximate Bayes Estimators 192
9 Local Asymptotic Normality for Discretely Observed
Homogeneous Diffusions 201
9.1 Introduction 201
9.2 Model, Assumptions and Preliminaries 202
9.3 Weak Convergence of the Approximate Likelihood Ratio
Random Fields 207
9.4 Asymptotics of Approximate Estimators and Bernstein von
Mises Type Theorems 221
9.5 Example: Logistic Diffusion 223
10 Estimating Function for Discretely Observed
Homogeneous Diffusions 225
10.1 Introduction 225
10.2 Rate of Consistency 233
10.3 Berry Esseen Bound 238
10.4 Examples 240
References 245
Index 263
|
| adam_txt |
Contents
Basic Notations XIII
1 Parametric Stochastic Differential Equations 1
Part I Continuous Sampling
2 Rates of Weak Convergence of Estimators in Homogeneous
Diffusions 15
2.1 Introduction 15
2.2 Berry Esseen Bounds for Estimators in the Ornstein
Uhlenbeck Process 16
2.3 Rates of Convergence in the Bernstein von Mises Theorem
for Ergodic Diffusions 26
2.4 Rates of Convergence of the Posterior Distributions
in Ergodic Diffusions 33
2.5 Berry Esseen Bound for the Bayes Estimator 41
2.6 Example: Hyperbolic Diffusion Model 47
3 Large Deviations of Estimators in Homogeneous
Diffusions 49
3.1 Introduction 49
3.2 Model, Assumptions and Preliminaries 50
3.3 Large Deviations for the Maximum Likelihood Estimator 51
3.4 Large Deviations for Bayes Estimators 57
3.5 Examples 59
4 Local Asymptotic Mixed Normality for Nonhomogeneous
Diffusions 61
4.1 Introduction 61
4.2 Model, Assumptions and Preliminaries 63
X Contents
4.3 Asymptotics of the Maximum Likelihood Estimator 67
4.4 The Bernstein von Mises Type Theorem and Asymptotics
of Bayes Estimators 68
4.5 Asymptotics of Maximum Probability Estimator 74
4.6 Examples 75
5 Bayes and Sequential Estimation in Stochastic PDEs 79
5.1 Long Time Asymptotics 79
5.1.1 Introduction 79
5.1.2 Model, Assumptions and Preliminaries 80
5.1.3 Bernstein von Mises Theorem 82
5.1.4 Asymptotics of Bayes Estimators 84
5.2 Sequential Estimation 85
5.2.1 Sequential Maximum Likelihood Estimation 85
5.2.2 Example 87
5.3 Spectral Asymptotics 88
5.3.1 Introduction 88
5.3.2 Model and Preliminaries 90
5.3.3 The Bernstein von Mises Theorem 93
5.3.4 Bayes Estimation 95
5.3.5 Example: Stochastic Heat Equation 96
6 Maximum Likelihood Estimation in Fractional
Diffusions 99
6.1 Introduction 99
6.2 Fractional Stochastic Calculus 100
6.3 Maximum Likelihood Estimation in Directly Observed
Fractional Diffusions 109
6.4 Maximum Likelihood Estimation in Partially Observed
Fractional Diffusions 113
6.5 Examples 118
Part II Discrete Sampling
7 Approximate Maximum Likelihood Estimation
in Nonhomogeneous Diffusions 125
7.1 Introduction 125
7.2 Model, Assumptions and Definitions 127
7.3 Accuracy of Approximations of the ltd and FS Integrals 135
7.4 Accuracy of Approximations of the Log likelihood Function . . . 142
7.5 Accuracy of Approximations of the Maximum Likelihood
Estimate 146
7.6 Example: Chan Karloyi Longstaff Sanders Model 148
7.7 Summary of Truncated Distributions 155
Contents XI
8 Rates of Weak Convergence of Estimators
in the Ornstein Uhlenbeck Process 159
8.1 Introduction 159
8.2 Notations and Preliminaries 160
8.3 Berry Esseen Type Bounds for AMLE1 162
8.4 Berry Esseen Type Bounds for AMLE2 173
8.5 Berry Esseen Type Bounds for Approximate Minimum
Contrast Estimators 178
8.6 Berry Esseen Bounds for Approximate Bayes Estimators 192
9 Local Asymptotic Normality for Discretely Observed
Homogeneous Diffusions 201
9.1 Introduction 201
9.2 Model, Assumptions and Preliminaries 202
9.3 Weak Convergence of the Approximate Likelihood Ratio
Random Fields 207
9.4 Asymptotics of Approximate Estimators and Bernstein von
Mises Type Theorems 221
9.5 Example: Logistic Diffusion 223
10 Estimating Function for Discretely Observed
Homogeneous Diffusions 225
10.1 Introduction 225
10.2 Rate of Consistency 233
10.3 Berry Esseen Bound 238
10.4 Examples 240
References 245
Index 263 |
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| index_date | 2024-07-02T19:01:02Z |
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| language | English |
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| series2 | Lecture notes in mathematics |
| spelling | Bishwal, Jaya P. N. Verfasser aut Parameter estimation in stochastic differential equations Jaya P. N. Bishwal Berlin [u.a.] Springer 2008 XI, 264 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1923 Equações diferenciais estocásticas larpcal Estimation d'un paramètre Processos estocásticos larpcal Équations différentielles stochastiques Parameter estimation Stochastic differential equations Parameterschätzung (DE-588)4044614-1 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s Parameterschätzung (DE-588)4044614-1 s DE-604 Lecture notes in mathematics 1923 (DE-604)BV000676446 1923 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016152924&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bishwal, Jaya P. N. Parameter estimation in stochastic differential equations Lecture notes in mathematics Equações diferenciais estocásticas larpcal Estimation d'un paramètre Processos estocásticos larpcal Équations différentielles stochastiques Parameter estimation Stochastic differential equations Parameterschätzung (DE-588)4044614-1 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4044614-1 (DE-588)4057621-8 |
| title | Parameter estimation in stochastic differential equations |
| title_auth | Parameter estimation in stochastic differential equations |
| title_exact_search | Parameter estimation in stochastic differential equations |
| title_exact_search_txtP | Parameter estimation in stochastic differential equations |
| title_full | Parameter estimation in stochastic differential equations Jaya P. N. Bishwal |
| title_fullStr | Parameter estimation in stochastic differential equations Jaya P. N. Bishwal |
| title_full_unstemmed | Parameter estimation in stochastic differential equations Jaya P. N. Bishwal |
| title_short | Parameter estimation in stochastic differential equations |
| title_sort | parameter estimation in stochastic differential equations |
| topic | Equações diferenciais estocásticas larpcal Estimation d'un paramètre Processos estocásticos larpcal Équations différentielles stochastiques Parameter estimation Stochastic differential equations Parameterschätzung (DE-588)4044614-1 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | Equações diferenciais estocásticas Estimation d'un paramètre Processos estocásticos Équations différentielles stochastiques Parameter estimation Stochastic differential equations Parameterschätzung Stochastische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016152924&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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