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Strong approximation of multiple Ito and Stratonovich stochastic integrals: multiple Fourier series approach
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 toExpand
Expansion of Iterated Stratonovich Stochastic Integrals of Arbitrary Multiplicity Based on Generalized Iterated Fourier Series Converging Pointwise
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 caseExpand
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
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 theExpand
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 stochasticExpand
Numerical Simulation of 2.5-Set of Iterated Ito Stochastic Integrals of Multiplicities 1 to 5 From the Taylor-Ito Expansion.
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, basedExpand
Expansion of Iterated Ito Stochastic Integrals of Arbitrary Multiplicity, Based on Generalized Multiple Fourier Series, Converging in the Mean
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 forExpand
Strong Numerical Methods of Order 3.0 for Ito Stochastic Differential Equations, Based on the Unified Stochastic Taylor Expansions and Multiple Fourier-Legendre Series
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 theExpand
A Comparative Analysis of Efficiency of Using the Legendre Polynomials and Trigonometric Functions for the Numerical Solution of Ito Stochastic Differential Equations
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 differentialExpand
New Representations of the Taylor–Stratonovich Expansion
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 newExpand
The unified Taylor-Ito expansion
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 ofExpand
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