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Strong approximation of multiple Ito and Stratonovich stochastic integrals: multiple Fourier series approach

- D. Kuznetsov
- Mathematics
- 2011

It is well known, that Ito stochastic differential equations (SDE) are adequate mathematical models of dynamic systems under the influence of random disturbances. One of the effective approaches to… Expand

Expansion of Iterated Stratonovich Stochastic Integrals of Arbitrary Multiplicity Based on Generalized Iterated Fourier Series Converging Pointwise

- D. Kuznetsov
- Mathematics
- 2 January 2018

The article is devoted to the expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity k (k ∈ N) based on generalized iterated Fourier series converging pointwise. The case… Expand

Explicit One-Step Strong Numerical Methods of Orders 2.0 and 2.5 for Ito Stochastic Differential Equations, Based on the Unified Taylor-Ito and Taylor-Stratonovich Expansions

- D. Kuznetsov
- Mathematics
- 8 February 2018

The article is devoted to explicit one-step numerical methods with strong order of convergence 2.5 for Ito stochastic differential equations with multidimensional non-additive noise. We consider the… Expand

On Numerical Modeling of the Multidimensional Dynamic Systems under Random Perturbations with the 1.5 and 2.0 Orders of Strong Convergence

- D. Kuznetsov
- Mathematics, Computer Science
- Autom. Remote. Control.
- 14 July 2018

The paper was devoted to developing numerical methods with the orders 1.5 and 2.0 of strong convergence for the multidimensional dynamic systems under random perturbations obeying stochastic… Expand

Numerical Simulation of 2.5-Set of Iterated Ito Stochastic Integrals of Multiplicities 1 to 5 From the Taylor-Ito Expansion.

- D. Kuznetsov
- Mathematics
- 15 October 2019

The article is devoted to the construction of effective procedures of the mean-square approximation of iterated Ito stochastic integrals of multiplicities 1 to 5 from the Taylor-Ito expansion, based… Expand

Expansion of Iterated Ito Stochastic Integrals of Arbitrary Multiplicity, Based on Generalized Multiple Fourier Series, Converging in the Mean

- D. Kuznetsov
- Mathematics
- 28 December 2017

The article is devoted to expansions of multiple Ito stochastic integrals, based on generalized multiple Fourier series converging in the mean. The method of generalized multiple Fourier series for… Expand

Strong Numerical Methods of Order 3.0 for Ito Stochastic Differential Equations, Based on the Unified Stochastic Taylor Expansions and Multiple Fourier-Legendre Series

- D. Kuznetsov
- Mathematics
- 5 July 2018

The article is devoted to explicit one-step numerical methods with strong order of convergence 3.0 for Ito stochastic differential equations with multidimensional non-additive noise. We consider the… Expand

A Comparative Analysis of Efficiency of Using the Legendre Polynomials and Trigonometric Functions for the Numerical Solution of Ito Stochastic Differential Equations

- D. Kuznetsov
- Mathematics
- 30 December 2018

The article is devoted to comparative analysis of the efficiency of application of Legendre polynomials and trigonometric functions to the numerical integration of Ito stochastic differential… Expand

New Representations of the Taylor–Stratonovich Expansion

- D. Kuznetsov
- Mathematics
- 1 December 2003

The problem of the Taylor–Stratonovich expansion of the Itô random processes in a neighborhood of a point is considered. The usual form of the Taylor–Stratonovich expansion is transformed to a new… Expand

The unified Taylor-Ito expansion

- O. Y. Kulchitski, D. Kuznetsov
- Mathematics
- 1 April 2000

We consider the problem of the Taylor-Ito expansion for Ito processes in a neighborhood of a fixed time moment. The Taylor-Ito expansion known in literature is unified by a canonical system of… Expand

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