Simulation methods for second order parabolic Cauchy problem
The Monte-Carlo algorithms for heat equation boundary problems based on heat potentials is well known when Laplace operator is the elliptic part of parabolic one [1], [2]. They essentially based on exact fundamental solution and cannot be used for heat equations when coefficient matrix is not constant. In this paper we construct and investigate simulation method for second order parabolic Cauchy problem when coefficient matrix is sufficiently smooth. There are constructed unbiased estimators for Cauchy problem solution and unbiased estimators for their functionals.