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Strong Approximation of Iterated Ito and Stratonovich Stochastic Integrals: Method of Generalized Multiple Fourier Series. Application to Numerical Solution of Ito SDEs and Semilinear SPDEs
Dmitriy F. Kuznetsov, Mikhail D. Kuznetsov
The monograph presents numerical integration techniques for Ito stochastic differential equations, focusing on high‑order strong methods (orders 1.0 to 3.0) and providing Python an…
New representations of the Hu-Meyer formulas and series expansion of iterated Stratonovich stochastic integrals with respect to components of a multidimensional Wiener process
Dmitriy F. Kuznetsov
The article is devoted to the systematic derivation of new representations of the Hu-Meyer formulas. The formula expressing a multiple Wiener stochastic integral through the sum of…
Expansions of Iterated Stratonovich Stochastic Integrals of Multiplicities 1 to 4. Combained Approach Based on Generalized Multiple and Iterated Fourier series
Dmitriy F. Kuznetsov
The article is devoted to the expansions of iterated Stratonovich stochastic integrals of multiplicities 1 to 4 on the base of the combined approach of generalized multiple and ite…
Expansions of Iterated Stratonovich Stochastic Integrals from the Taylor-Stratonovich Expansion, Based on Multiple Trigonometric Fourier Series. Comparison With the Milstein Expansion
Dmitriy F. Kuznetsov
The article is devoted to comparison of the Milstein expansion of iterated Stratonovich stochastic integrals with the method of expansion of iterated stochastic integrals based on…
Expansion of Iterated Stratonovich Stochastic Integrals of Multiplicity 2 Based on Double Fourier-Legendre Series Summarized by Pringsheim Method
Dmitriy F. Kuznetsov
The article is devoted to the expansion of iterated Stratonovich stochastic integrals of second multiplicity into the double series of products of standard Gaussian random variable…
Expansion of Iterated Stratonovich Stochastic Integrals of Multiplicity 3 Based on Generalized Multiple Fourier Series Converging in the Mean: General Case of Series Summation
Dmitriy F. Kuznetsov
The article is devoted to the development of the method of expansion and mean-square approximation of iterated Ito stochastic integrals based on generalized multiple Fourier series…