Corpus ID: 54897946

# Expansion of Multiple Stochastic Integrals According to Martingale Poisson Measures and According to Martingales, Based on Generalized Multiple Fourier Series

@article{Kuznetsov2018ExpansionOM,
title={Expansion of Multiple Stochastic Integrals According to Martingale Poisson Measures and According to Martingales, Based on Generalized Multiple Fourier Series},
author={D. Kuznetsov},
journal={arXiv: Probability},
year={2018}
}
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 of multiple stochastic integrals according to martingale Poisson measures is obtained. For the multiple stochastic integrals according to martingales we have proven two theorems. The first theorem is the generalization of expansion of multiple Ito stochastic integrals of arbitrary multiplicity, based on… Expand
6 Citations
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 Iterated Stratonovich Stochastic Integrals of Fifth Multiplicity, Based on Generalized Multiple Fourier Series
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 expansionExpand
New Simple Method for Obtainment an Expansion of Double Stochastic Ito integrals, Based on the Expansion of Brownian Motion Using Legendre polynomials and Trigonometric Functions.
The atricle is devoted to the new simple method for obtainment an expansion of double stochastic Ito integrals, based on the expansion of Brownian motion (standard Wiener process) using completeExpand
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
New Representation of Levy Stochastic Area, Based on Legendre polynomials
The article is devoted to obtainment a new representation of Levy stochastic area, based on Legengre polynomials. We use expansion of multiple Ito stochastic integrals, based on multipleExpand
Expansions of Iterated Stratonovich Stochastic Integrals of Multiplicities 1 to 4, Based on Generalized Multiple Fourier Series
The article is devoted to the expansions of iterated Stratonovich stochastic integrals of multiplicities 1 to 4 on the basis of the method of generalized multiple Fourier series. Mean-squareExpand

#### References

SHOWING 1-10 OF 21 REFERENCES
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 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
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
Numerical integration of stochastic differential equations — ii
• Mathematics
• The Bell System Technical Journal
• 1981
In a previous paper, a method was presented to integrate numerically nonlinear stochastic differential equations (SDEs) with additive, Gaussian, white noise. The method, a generalization of the RangeExpand
Numerical Integration of Stochastic Differential Equations
This chapter provides an introduction into the numerical integration of stochastic differential equations (SDEs). Again X t denotes a stochastic process and solution of an SDE, \frac{{\partialExpand
Stochastic Differential Equations and its Applications
• Naukova Dumka, Kiev,
• 1982
Expansion of Multiple Itô Stochastic Integrals of Arbitrary Multiplicity, Based on Generalized Multiple Fourier Series
• Converging in the Mean
• 2017
Multiple Itô and Stratonovich Stochastic Integrals: Fourier-Legendre and Trigonometric Expansions, Approximations, Formulas. [In English
• Electronic Journal Differential Equations and Control Processes,
• 2017
Multiple Itô and Stratonovich Stochastic Integrals: Approximations, Properties, Formulas. [In English
• Polytechnical University Publishing House, St.-Petersburg,
• 2013
Multiple Itô and Stratonovich Stochastic Integrals and Multiple Fourier Series
• Electronic Journal "Differential Equations and Control Processes
• 2010