Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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   The article is devoted to the expansion of iterated Ito stochastic integrals
of second multiplicity 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 was
first derived in the author's work (1997). In this article, we obtain the
mentioned representation by a simpler method compared to the author's work
(1997). Also, we get the polynomial representation of the Levy stochastic area
using the method of expansion of iterated Ito stochastic integrals based on
generalized multple Fourier series. The polynomial representation of the Levy
stochastic area has more simple form in comparison with the classical
trigonometric representation of the Levy stochastic area. The convergence in
the mean of degree $2n$ $(n\in\mathbb{N})$ as well as the convergence with
probability 1 for approximations of the Levy stochastic area are proved. The
results of the article can be applied to the numerical solution of Ito
stochastic differential equations as well as to the numerical approximation of
mild solution for non-commutative semilinear stochastic partial differential
equations.

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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph