Numerical Solution of Stochastic Differential Equations
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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Contents
Preliminaries
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1 |
5
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6 |
1
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13 |
3
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23 |
6
|
26 |
8
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40 |
Probability and Stochastic Processes
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51 |
Stochastic Differential Equations
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75 |
Introduction to Stochastic
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305 |
63
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308 |
Strong Approximations
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336 |
68
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351 |
Explicit Strong Approximations
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373 |
Implicit Strong Approximations
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395 |
Selected Applications
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426 |
Weak Approximations
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457 |
Stochastic Differential Equations
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103 |
7
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108 |
9
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119 |
51
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125 |
Stochastic Taylor Expansions
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161 |
of Truncated StratonovichTaylor Expansions
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210 |
Applications of Stochastic Differential Equations
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227 |
4
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241 |
Applications of Stochastic Differential Equations
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253 |
9
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271 |
Time Discrete Approximations
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276 |
Other editions - View all
Numerical Solution of Stochastic Differential Equations Peter E. Kloeden,Eckhard Platen Limited preview - 2011 |
Numerical Solution of Stochastic Differential Equations Peter E. Kloeden,Eckhard Platen No preview available - 2010 |
Common terms and phrases
1-dimensional Chapter component constant continuous corresponding defined density derivatives deterministic diffusion coefficient diffusion process discrete approximation discretization error dW₁ dX₁ estimate Euler approximation Euler method Euler scheme evaluated example Exercise finite function f implicit inequality initial value interval Ito formula Ito integrals Ito process Ito-Taylor expansion Lebesgue Lemma linear Lyapunov Lyapunov exponents Markov chain matrix mean-square Milstein scheme multi-indices multiple Ito integrals multiple Stratonovich integrals obtain order 1.5 strong ordinary differential equation parameter Platen probability space proof random number random variables Results of PC-Exercise sample paths satisfies scalar Section simulations solution stability standard Wiener process step stochastic differential equation stochastic integrals stochastic process Stratonovich integrals strong scheme subsets Talay Theorem Tn+1 variance vector W₁ Wiener process X₁ Y₁ Yn+1