Подробное описание документа

Kuznetsov D. F.
   Strong Approximation of Multiple Ito and Stratonovich Stochastic Integrals: Multiple Fourier Series Approach / Kuznetsov D. F. ; Sant-Petersburg State Polytechnical University. - 2nd ed. - Saint-Petersburg : Publishing house of the Polytechnical University, 2011. - 282 с. - ISBN 978-5-7422-3162-2.

Тhis book is the first monograph Where the problem of strong (mean-square) approximation of multiple Ito and Stratonovich stochastic integrals is sistematically analyzed in tlle context of numerical integration of stochastic differential Ito equations.
Тhis monograph for the first time successfully usе the tool of multiple and iterative Fourier series, built in the sрасе L2 and poitwise, for the strong approximation of multiple stochastic integrals. Тhе aforesaid means were not used in this academic field before.
We obtained а general result connected with expansion of multiple stochastic Ito integrals witll any fixed multiplicity k, based оп generalized multiple Fourier series converging in the sрасе L2([t, T]k). Тhis result is adapted for multiple Stratpnovich stochastic integralsof 1 - 4 mllltiplicity for Legendre polynomial system and system of trigonometric functions, as well as for other types of multiple stосhаstiс integrals. Тhе theorem оn expansion of multiple Stratonovich stochastic integrals with any fixed multiplicity k, based оп generalized Fourier series converging pointwise is verified. We obtained exact expressions for mean-square errors of approximation of multiрlе stochastic Ito integrals of 1 - 4 multiplicity. We provided а significant practical material devoted to expansion and approximation of specific multiple Ito and Stratonovich stochastic integrals of 1 - 5 multiplicity using the system of Legendre polynomials and the system of trigonometric functions. We compared the methods formulated in this book with existing methods of strong approximation of multiple stochastic integrals.
Тhis monograph open а new direction in researching of multiple Ito and Stratonovich stochastic integrals. Тhis book will bе interesting for specialists dealing with the theory of stochastic processes, applied and computational mathematics, senior students and postgraduates of technical institutes and universities, as well as for computer experts.