Corpus ID: 209955789

# Expansion of Iterated Stratonovich Stochastic Integrals of Fifth Multiplicity, Based on Generalized Multiple Fourier Series

@article{Kuznetsov2018ExpansionOI,
title={Expansion of Iterated Stratonovich Stochastic Integrals of Fifth Multiplicity, Based on Generalized Multiple Fourier Series},
author={D. F. Kuznetsov},
journal={arXiv: Probability},
year={2018}
}
The article is devoted to the construction of expansion of iterated Stratonovich stochastic integrals of fifth multiplicity, based on the method of generalized multiple Fourier series. This expansion converges in the mean-square sense and contains only one operation of the limit transition in contrast to its existing analogues. The expansion of iterated Stratonovich stochastic integrals turned out much simpler, than the appropriate expansion of iterated Ito stochastic integrals. We use the… Expand
26 Citations
Expansion of Multiple Stratonovich Stochastic Integrals of Arbitrary Multiplicity, Based on Generalized Repeated Fourier Series, Converging Pointwise
The article is devoted to the expansion of multiple Stratonovich stochastic integrals of arbitrary multiplicity $k$, based on the generalized repeated Fourier series. The case of Fourier-LegendreExpand
Expansion of Iterated Stratonovich Stochastic Integrals of Multiplicity 2 Based on Double Fourier-Legendre Series Summarized by Pringsheim Method
Abstract. 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 variables. TheExpand
Numerical Simulation of 2.5-Set of Iterated Stratonovich Stochastic Integrals of Multiplicities 1 to 5 From the Taylor-Stratonovich Expansion
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 the method ofExpand
Expansions of Multiple Stratonovich Stochastic Integrals From the Taylor-Stratonovich Expansion, Based on Multiple Trigonometric Fourier Series. Comparison With the Milstein Expansion
The article is devoted to comparison of the Milstein expansion of multiple stochastic integrals with the method of expansion of multiple stochastic integrals, based on generalized multiple FourierExpand
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
Expansion of Multiple Stratonovich Stochastic Integrals of Multiplicity 2, Based on Double Fourier-Legendre Series, Summarized by Prinsheim Method
The article is devoted to the expansion of multiple Stratonovich stochastic integrals of multiplicity 2 into double series of standard Gaussian random variables. The proof of the expansion is basedExpand
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
• Computational Mathematics and Mathematical Physics
• 2019
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
Application of the Method of Approximation of Iterated Stochastic Ito Integrals Based on Generalized Multiple Fourier Series to the High-Order Strong Numerical Methods for Non-Commutative Semilinear Stochastic Partial Differential Equations
We consider a method for the approximation of iterated stochastic Ito integrals of arbitrary multiplicity $k$ $(k\in \mathbb{N})$ with respect to the infinite-dimensional Wiener process using theExpand
Exact Calculation of Mean-Square Error of Approximation of Multiple Ito Stochastic integrals for the Method, Based on the Multiple Fourier Series
The article is devoted to the obtainment of exact and approximate expressions for mean-square error of approximation of multiple Ito stochastic integrals from the stochastic Taylor-Ito expansion 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

#### References

SHOWING 1-10 OF 94 REFERENCES
Expansion of iterated Stratonovich stochastic integrals based on generalized multiple Fourier series
The article is devoted to expansions of iterated Stratonovich stochastic integrals of multiplicities 1-4 on the base of the method of generalized multiple Fourier series. We prove the mean-squareExpand
Expansion of Iterated Stratonovich Stochastic Integrals of Multiplicity 2 Based on Double Fourier-Legendre Series Summarized by Pringsheim Method
Abstract. 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 variables. TheExpand
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
The Hypothesis About Expansion of Multiple Stratonovich Stochastic Integrals of Arbitrary Multiplicity
In this review article we collected more than ten theorems about expansions of multiple Ito and Stratonovich stochastic integrals, which was formulated and proved by the author. These theorems open aExpand
Expansion of Multiple Stratonovich Stochastic Integrals of Multiplicity 2, Based on Double Fourier-Legendre Series, Summarized by Prinsheim Method
The article is devoted to the expansion of multiple Stratonovich stochastic integrals of multiplicity 2 into double series of standard Gaussian random variables. The proof of the expansion is basedExpand
The Proof of Convergence with Probability 1 in the Method of Expansion of Iterated Ito Stochastic Integrals Based on Generalized Multiple Fourier Series
The article is devoted to the formulation and proof of the theorem on convergence with probability 1 of expansion of iterated Ito stochastic integrals of arbitrary multiplicity based on generalizedExpand
Mean-Square Approximation of Multiple Ito and Stratonovich Stochastic Integrals from the Taylor-Ito and Taylor-Stratonovich Expansions, Using Legendre Polynomials
The article is devoted to material about expansions and mean-square approximations of specific multiple Ito and Stratonovich stochastic integrals using multiple Fourier-Legendre series. ConsideredExpand
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
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
• Computational Mathematics and Mathematical Physics
• 2019
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
Expansion of Multiple Stochastic Integrals According to Martingale Poisson Measures and According to Martingales, Based on Generalized Multiple Fourier Series
In the article we consider some versions of the approach to expansion of multiple Ito stochastic integrals of arbitrary multiplicity, based on generalized multiple Fourier series. The expansion ofExpand