A strong and weak approximation scheme for stochastic differential equations driven by a time-changed Brownian motion
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.
Cite
@article{arxiv.1408.4377,
title = {A strong and weak approximation scheme for stochastic differential equations driven by a time-changed Brownian motion},
author = {Ernest Jum and Kei Kobayashi},
journal= {arXiv preprint arXiv:1408.4377},
year = {2015}
}
Comments
19 pages, 3 figures. To appear in Probability and Mathematical Statistics. Sections reorganized; statements of Proposition 3 and Theorems 11 and 13 improved; text rewritten in a succinct form; typos corrected; references added; author contact information updated