40 citations · 312 across the 28 of their papers we have counts for
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Strong Numerical Methods of Orders 2.0, 2.5, and 3.0 for Ito Stochastic Differential Equations Based on the Unified Stochastic Taylor Expansions and Multiple Fourier-Legendre Series
Dmitriy F. Kuznetsov
The article is devoted to the construction of explicit one-step numerical methods with the strong orders of convergence 2.0, 2,5, and 3.0 for Ito stochastic differential equations…
New Simple Method of Expansion of Iterated Ito Stochastic integrals of Multiplicity 2 Based on Expansion of the Brownian Motion Using Legendre Polynomials and Trigonometric Functions
Dmitriy F. Kuznetsov
The article is devoted to the expansion of iterated Ito stochastic integrals of second multiplicity based on expansion of the Brownian motion (standard Wiener process) using comple…
Numerical Simulation of 2.5-Set of Iterated Stratonovich Stochastic Integrals of Multiplicities 1 to 5 From the Taylor-Stratonovich Expansion
Dmitriy F. Kuznetsov
The article is devoted to construction of effective procedures of the mean-square approximation for iterated Stratonovich stochastic integrals of multiplicities 1 to 5. We apply th…
Expansion of Iterated Stratonovich Stochastic Integrals of Fifth, Sixth, Seventh and Eighth Multiplicities Based on Generalized Multiple Fourier Series
Dmitriy F. Kuznetsov
The article is devoted to the construction of expansions of iterated Stratonovich stochastic integrals of fifth, sixth, seventh and eighth multiplicities based on the method of gen…
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. Combined Approach Based on Generalized Multiple and Iterated Fourier Series
Dmitriy F. Kuznetsov
The article is devoted to the expansion of iterated Stratonovich stochastic integrals of multiplicity 2 on the base of the combined approach of generalized multiple and iterated Fo…
Expansion of Iterated Stochastic Integrals with Respect to Martingale Poisson Measures and with Respect to Martingales Based on Generalized Multiple Fourier Series
Dmitriy F. Kuznetsov
We consider some versions and generalizations of an approach to the expansion of iterated Ito stochastic integrals of arbitrary multiplicity based on general…
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…
Integration Order Replacement Technique for Iterated Ito Stochastic Integrals and Iterated Stochastic Integrals With Respect to Martingales
Dmitriy F. Kuznetsov
The article is devoted to the integration order replacement technique for iterated Ito stochastic integrals and iterated stochastic integrals with respect to martingales. We consid…
The Hypotheses on Expansion of Iterated Stratonovich Stochastic Integrals of Arbitrary Multiplicity and Their Partial Proof
Dmitriy F. Kuznetsov
In this article, we collected more than thirty theorems on expansions of iterated Ito and Stratonovich stochastic integrals, which have been formulated and proved by the author in…
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…
Exact Calculation of the Mean-Square Error in the Method of Expansion of Iterated Ito Stochastic integrals Based on Generalized Multiple Fourier Series
Dmitriy F. Kuznetsov
The article is devoted to the developement of the method of expansion and mean-square approximation of iterated Ito stochastic integrals based on generalized multiple Fourier serie…
Expansion of Iterated Stratonovich Stochastic Integrals of Arbitrary Multiplicity Based on Generalized Iterated Fourier Series Converging Pointwise
Dmitriy F. Kuznetsov
The article is devoted to the expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity based on the generalized iterated Fourier ser…
Mean-Square Approximation of Iterated Ito and Stratonovich Stochastic Integrals of Multiplicities 1 to 6 from the Taylor-Ito and Taylor-Stratonovich Expansions Using Legendre Polynomials
Dmitriy F. Kuznetsov
The article is devoted to the practical material on expansions and mean-square approximations of specific iterated Ito and Stratonovich stochastic integrals of multiplicities 1 to…