Corpus ID: 224792841

# 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.

@article{Kuznetsov2020NewSM,
title={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.},
author={D. Kuznetsov},
journal={arXiv: Probability},
year={2020}
}
The atricle is devoted to the new simple method for obtainment an expansion of iterated Ito stochastic integrals of multiplicity 2 based on expansion of the Brownian motion (standard Wiener process) using complete orthonormal systems of functions in the space $L_2([t, T]).$ The cases of Legendre polynomials and trigonometric functions are considered in details. We obtained a new representation of the Levy stochastic area based on the Legendre polynomials. This representation also has been… Expand
2 Citations
Exact Calculation of the Mean-Square Error in the Method of Approximation of Iterated Ito Stochastic integrals, Based on Generalized Multiple Fourier Series
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Expansion of Iterated Stratonovich Stochastic Integrals of Multiplicity 3, Based on Generalized Multiple Fourier Series, Converging in the Mean: General Case of Series Summation
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, converging inExpand

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