A tamed-adaptive Milstein scheme for stochastic differential equations with low regularity coefficients

2024/11/04 by T.B. Vu, Hoang-Long Ngo, Vu, Thi-Huong +5
Economics, Econometrics and Finance · Social Sciences · #Stochastic processes and financial applications #Insurance, Mortality, Demography, Risk Management

paper · pdf · doi:10.48550/arxiv.2411.01849

Abstract

We propose a tamed-adaptive Milstein scheme for stochastic differential equations in which the first-order derivatives of the coefficients are locally Hölder continuous of order α. We show that the scheme converges in the L₂-norm with a rate of (1+α)/2 over both finite intervals [0, T] and the infinite interval (0, +∞), under certain growth conditions on the coefficients.

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