A strong and weak approximation scheme for stochastic differential equations driven by a time-changed Brownian motion

2014/08/19 by Ernest Jum, Kei Kobayashi, Jum, Ernest +1 · 3 citations
Economics, Econometrics and Finance · Mathematics · Social Sciences · #60H10 #60H35 #65C30 #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Statistical Distribution Estimation and Applications #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1408.4377

openalex publication_date 2014/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper establishes a discretization scheme for a large class of stochastic differential equations driven by a time-changed Brownian motion with drift, where the time change is given by a general inverse subordinator. The scheme involves two types of errors: one generated by application of the Euler-Maruyama scheme and the other ascribed to simulation of the inverse subordinator. With the two errors carefully examined, the orders of strong and weak convergence are derived. Numerical examples are attached to support the convergence results.

Cited by

• α-scaled strong convergence of stochastic theta method for stochastic differential equations driven by time-changed Lévy noise beyond Lipschitz continuity
• 1/2 order convergence rate of Euler-type methods for time-changed stochastic differential equations with super-linearly growing drift and diffusion coefficients
• Strong approximation of time-changed stochastic differential equations involving drifts with random and non-random integrators

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