Compensated projected Euler-Maruyama method for stochastic differential equations with superlinear jumps

Highlights：

• The project EM method is extended to SDEs with superlinear jumps.

• A convergence result is derived by using ideas of C-stability and B-consistency, so that moment-bounded proof of the numerical solution can be avoided.

• Since the Poisson increment N(t)−N(s) has all moments of order O(t−s)for all 0≤s≤t<∞, some new techniques are developed for convergence analysis.

• Compared with most of the existing works on numerical convergence, we allow the jump coefficient to grow superlinearly under appropriate assumptions.

• The projected EM method is essentially explicit, so it can reach strong convergence of order close to 1/2 with a cheap computational cost.

摘要

•The project EM method is extended to SDEs with superlinear jumps.•A convergence result is derived by using ideas of C-stability and B-consistency, so that moment-bounded proof of the numerical solution can be avoided.•Since the Poisson increment N(t)−N(s) has all moments of order O(t−s)for all 0≤s≤t<∞, some new techniques are developed for convergence analysis.•Compared with most of the existing works on numerical convergence, we allow the jump coefficient to grow superlinearly under appropriate assumptions.•The projected EM method is essentially explicit, so it can reach strong convergence of order close to 1/2 with a cheap computational cost.

论文关键词：Stochastic differential equations with jumps,Compensated projected Euler-Maruyama method,Mean square convergence,C-stability,B-consistency

论文评审过程：Received 29 April 2020, Revised 5 October 2020, Accepted 18 October 2020, Available online 18 November 2020, Version of Record 18 November 2020.