Kloeden P/, Platen E., Schurz H. — Numerical solution of SDE through computer experiments
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Название: Numerical solution of SDE through computer experiments
Авторы: Kloeden P/, Platen E., Schurz H.
Аннотация:
The book provides an easily accessible computationally oriented introduction into the numerical solution of stochastic differential equations using computer experiments. It develops in the reader an ability to apply numerical methods solving stochastic differential equations in their own fields. Furthermore, it creates an intuitive understanding of the necessary theoretical background from stochastic and numeric analysis. A downloadable softward containing programs for over 100 problems is provided at each of the following homepages:
to enable the reader to develop an intuitive understanding of the issues involved. Applications include stochastic dynamical systems, filtering, parametric estimation and finance modeling.
The book is intended for readers without specialist stochastic background who want to apply such numerical methods to stochastic differential equations that arise in their own filed.
Taylor method truncated101 Taylor scheme203 Taylor scheme, 1.5 strong146147 Taylor scheme, 2.0 strong148 Taylor scheme, 2.0 weak181203 Taylor scheme, 2.0 weak simplified182 Taylor scheme, 3.0 weak simplified183204 Taylor scheme, 4.0 weak simplified184205 Taylor scheme, bilinear 2.0171 Taylor scheme, implicit 1.5 strong162 Taylor scheme, implicit 2.0 strong163 Taylor scheme, implicit 2.0 weak197 Taylor scheme, weak179 Telegraphic noise process244 Test for independence40 Test function27 Time approximation discrete91111 Time discretization91110 Trajectory43 Transition matrix43 Transition probability44 Trapezoidal method98 Trapezoidal method, modified98 Two-step scheme, implicit strong order 1.0167 Two-step scheme, implicit strong order 1.5167 Two-step scheme, implicit strong order 2.0168 Two-step scheme, strong order 1.0155 Two-step scheme, strong order 1.5156 U(a,b), uniformly distributed on [a,b]4 Uniformly distributed417 Var(X), variance of X17 Variance17222655 Variance reducing approximations207 Variance reducing estimators209 Variance reduction method207251 Variance reduction technique251 Vector version Ito formula73 Visualization219 Volatility265 W(t), , Wiener process at time t50 w.p.1, with probability one227 Waiting time48 Weak convergence27 Weak convergence, order 128 Weak Taylor approximation order 1.0179 Weak Taylor scheme180 Weak Taylor scheme, order 2.0181 Weak Taylor scheme, order 2.0 implicit195 Weak Taylor scheme, order 2.0 simplified182 Weak Taylor scheme, order 3.0 simplified183 Weak Taylor scheme, order 4.0 simplified184 Wiener process50555664 Wiener process, m-dimensional7381 Wiener process, standard50 Wiener process, tied-down59 With probability one (w.p.1)2 Zakai equation239 [a,b], closed interval from a to b4
, Wiener process at time t 
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