Numerical Solution of Stochastic Differential Equations

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Springer Science & Business Media, 17.04.2013 - 636 Seiten
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.
 

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Inhalt

Preliminaries
1
Probability and Stochastic Processes
51
Stochastic Differential Equations
75
Stochastic Differential Equations
103
Stochastic Taylor Expansions
161
Applications of Stochastic Differential Equations
227
Applications of Stochastic Differential Equations
253
Time Discrete Approximations
276
Implicit Strong Approximations
395
Selected Applications
426
Weak Approximations
457
Explicit and Implicit Weak Approximations
485
Variance Reduction Methods
511
Selected Applications of Weak Approximations
529
Solutions of Exercises
549
Bibliographical Notes
587

Introduction to Stochastic
305
Strong Approximations
336
Explicit Strong Approximations
373

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