The weak rate of convergence for the Euler-Maruyama approximation of\n one-dimensional stochastic differential equations involving the local times\n of the unknown process

2017/01/02 by Mohsine Benabdallah, Benabdallah, Mohsine, Kamal Hiderah +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #41A25 #60H10 #60H35 #60J55 #65C30 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Numerical Analysis (math.NA) #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1701.00551

openalex publication_date 2017/01/02 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the weak convergence of the Euler-Maruyama\napproximation for one dimensional stochastic differential equations involving\nthe local times of the unknown process. We use a transformation in order to\nremove the local time from the stochastic differential equations and we provide\nthe approximation of Euler-maruyama for the stochastic differential equations\nwithout local time. After that, we conclude the approximation of Euler-maruyama\nfor one dimensional stochastic differential equations involving the local times\nof the unknown process , and we provide the rate of weak convergence for any\nfunction G in a certain class.\n

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