2016/09/20 by Jianhai Bao, Xing Huang, Bao, Jianhai +3
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #41A25 #60C30 #60H10 #60H35 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1609.06080
openalex publication_date 2016/09/20 · openalex created_date 2016/09/30 · openalex updated_date 2026/07/28
In this paper, we are concerned with convergence rate of Euler-Maruyama scheme for stochastic differential equations with rough coefficients. The key contributions lie in (i), by means of regularity of non-degenerate Kolmogrov equation, we investigate convergence rate of Euler-Maruyama scheme for a class of stochastic differential equations, which allow the drifts to be Dini-continuous and unbounded; (ii) by the aid of regularization properties of degenerate Kolmogrov equation, we discuss convergence rate of Euler-Maruyama scheme for a range of degenerate stochastic differential equations, where the drift is locally Hölder-Dini continuous of order (2)/(3) with respect to the first component, and is merely Dini-continuous concerning the second component.