Random walk numerical scheme for the steady-state of stochastic differential equations

The continuous-time random walk (CTRW) scheme is a time-continuous and space-discretization method to obtain the numerical solution of stochastic differential equations (SDEs). Compared with the traditional time-discretization scheme, it has the advantages of numerical stability and can alleviate the curse of dimensionality. This paper proposes an improved version of the CTRW scheme for the numerical solution of SDEs. By compensating the artificial diffusion caused by the Poisson approximation of the drift term of the SDE, the improved CTRW scheme has significantly better performance in the weak noise case, especially in approximating the invariant probability measure. Numerical studies show that the improved CTRW scheme has more accuracy than the existing one but takes less computation time. In addition, it has better accuracy of the mean holding time. We also modify the hybrid Fokker-Planck solver proposed for the CTRW scheme to compute the invariant probability measure.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This paper proposes an improved version of the continuous-time random walk (CTRW) scheme for the numerical solution of stochastic differential equations (SDEs). The improved CTRW scheme compensates for artificial diffusion caused by the Poisson approximation, resulting in significantly better performance in weak noise cases and approximating the invariant probability measure. Numerical studies demonstrate that the improved CTRW scheme is more accurate and computationally efficient compared to existing schemes, and it also improves the accuracy of the mean holding time. Additionally, the hybrid Fokker-Planck solver used for computing the invariant probability measure is modified.