Numerical approximations of one-point large deviations rate functions of stochastic differential equations with small noise
Jialin Hong,
Diancong Jin,
Derui Sheng
Abstract:In this paper, we study the numerical approximation of the one-point large deviations rate functions of nonlinear stochastic differential equations (SDEs) with small noise. We show that the stochastic θ-method satisfies the one-point large deviations principle with a discrete rate function for sufficiently small step-size, and present a uniform error estimate between the discrete rate function and the continuous one on bounded sets in terms of step-size. It is proved that the convergence orders in the cases of… Show more
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