Mean Square Approximation of Solutions of Stochastic Differential Equations Using Legendre's Polynomials

摘要

We consider approximation for iterated Stratonovich stochastic integrals using multiple Fourier series in terms of Legendre polynomials. We have obtained approximations of stochastic integrals of the multiplicity 1-5. We consider root-mean-square convergence of approximation of iterated stochastic integrals.