Expansion of Iterated Stratonovich Stochastic Integrals of Arbitrary Multiplicity Based on Generalized Iterated Fourier Series Converging Pointwise

Understand

The article is devoted to the expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity $k$ $(k\in\mathbb{N})$ based on the generalized iterated Fourier series converging pointwise.

• The case of Fourier-Legendre series as well as the case of trigonometric Fourier series are considered in details.
• The obtained expansion provides a possibility to represent the iterated Stratonovich stochastic integral in the form of iterated series of products of standard Gaussian random variables.
• Convergence in the mean of degree $2n$ $(n\in \mathbb{N})$ of the expansion is proved.