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Stochastic versus Deterministic Systems of Differential Equations : Chapman & Hall/CRC Pure and Applied Mathematics - G. S. Ladde

Stochastic versus Deterministic Systems of Differential Equations

Chapman & Hall/CRC Pure and Applied Mathematics

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This peerless reference/text unfurls a unified and systematic study of the two types of mathematical models of dynamic processes-stochastic and deterministic-as placed in the context of systems of stochastic differential equations. Using the tools of variational comparison, generalized variation of constants, and probability distribution as its methodological backbone, Stochastic Versus Deterministic Systems of Differential Equations addresses questions relating to the need for a stochastic mathematical model and the between-model contrast that arises in the absence of random disturbances/fluctuations and parameter uncertainties both deterministic and stochastic.

Preface
Notation and Abbreviations
Random Polynomials
Introductionp. 1
Upper Bound for Mean Deviationp. 1
Error Estimatesp. 4
Eigenvalues of Random Matricesp. 10
Stability of Random Matricesp. 21
Applicationsp. 24
Numerical Examplesp. 27
Notes and Commentsp. 35
Ordinary Differential Systems with Random Parameters
Introductionp. 37
Variation of Constants Methodp. 38
Comparison Methodp. 45
Probability Distribution Methodp. 58
Stability Analysisp. 66
Error Estimatesp. 83
Relative Stabilityp. 100
Applications to Population Dynamicsp. 110
Numerical Examplesp. 122
Notes and Commentsp. 129
Boundary Value Problems with Random Parameters
Introductionp. 131
Green's Function Methodp. 132
Comparison Methodp. 139
Probability Distribution Methodp. 150
Solvability and Uniqueness Analysisp. 165
Stability Analysisp. 169
Error Estimatesp. 174
Relative Stabilityp. 180
Applications to Physical Systemsp. 184
Numerical Examplesp. 213
Notes and Commentsp. 217
Ito-Type Stochastic Differential Systems
Introductionp. 219
Variation of Constants Methodp. 220
Comparison Methodp. 227
Probability Distribution Methodp. 234
Stability Analysisp. 238
Error Estimatesp. 245
Relative Stabilityp. 252
Applications to Population Dynamicsp. 255
Numerical Examplesp. 262
Notes and Commentsp. 266
Boundary Value Problems of Ito-Type
Introductionp. 267
Green's Function Methodp. 267
Stability Analysisp. 277
Error Estimatesp. 280
Relative Stabilityp. 285
Notes and Commentsp. 287
Introductionp. 289
Convergence of Random Sequencesp. 289
Initial Value Problemsp. 291
Boundary Value Problemsp. 298
Referencesp. 301
Indexp. 313
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780824746971
ISBN-10: 082474697X
Series: Chapman & Hall/CRC Pure and Applied Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 300
Published: 5th December 2003
Country of Publication: US
Dimensions (cm): 27.9 x 21.6  x 1.91
Weight (kg): 0.59
Edition Number: 1