Numerical Solution of Stochastic Differential Equations

Front Cover
Springer Science & Business Media, Apr 17, 2013 - Mathematics - 636 pages
The aim of this book is to provide an accessible introduction to stochastic differ ential equations and their applications together with a systematic presentation of methods available for their numerical solution. During the past decade there has been an accelerating interest in the de velopment of numerical methods for stochastic differential equations (SDEs). This activity has been as strong in the engineering and physical sciences as it has in mathematics, resulting inevitably in some duplication of effort due to an unfamiliarity with the developments in other disciplines. Much of the reported work has been motivated by the need to solve particular types of problems, for which, even more so than in the deterministic context, specific methods are required. The treatment has often been heuristic and ad hoc in character. Nevertheless, there are underlying principles present in many of the papers, an understanding of which will enable one to develop or apply appropriate numerical schemes for particular problems or classes of problems.
 

Contents

Preliminaries
1
5
6
1
13
3
23
6
26
8
40
Probability and Stochastic Processes
51
Stochastic Differential Equations
75
Introduction to Stochastic
305
63
308
Strong Approximations
336
68
351
Explicit Strong Approximations
373
Implicit Strong Approximations
395
Selected Applications
426
Weak Approximations
457

Stochastic Differential Equations
103
7
108
9
119
51
125
Stochastic Taylor Expansions
161
of Truncated StratonovichTaylor Expansions
210
Applications of Stochastic Differential Equations
227
4
241
Applications of Stochastic Differential Equations
253
9
271
Time Discrete Approximations
276
Explicit and Implicit Weak Approximations
485
Variance Reduction Methods
511
Selected Applications of Weak Approximations
529
Solutions of Exercises
549
Bibliographical Notes
587
75
604
81
613
96
621
Index
629
103
630
Copyright

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