Statistics for Stochastic Differential Equations and Approximations of Resolvent

The numerical evaluation of statistics plays a crucial role in statistical physics and its applied fields. It is possible to evaluate the for stochastic differential equation with Gaussian white noise via corresponding backward Kolmogorov equation. important notice that there no need obtain solution on whole domain; it enough value at certain point corresponds initial coordinate For this aim, an algorithm based combinatorics has recently been developed. In paper, we discuss higher-order approximation resolvent, second-order proposed. proposed shows convergence. Furthermore, convergence property naive algorithms naturally leads extrapolation methods; they work well calculate more accurate fewer computational costs. method demonstrated Ornstein–Uhlenbeck process noisy van der Pol system.