Strong approximation of time-changed stochastic differential equations involving drifts with random and non-random integrators
Abstract
The rates of strong convergence for various approximation schemes are investigated for a class of stochastic differential equations (SDEs) which involve a random time change given by an inverse subordinator. SDEs to be considered are unique in two different aspects: i) they contain two drift terms, one driven by the random time change and the other driven by a regular, non-random time variable; ii) the standard Lipschitz assumption is replaced by that with a time-varying Lipschitz bound. The difficulty imposed by the first aspect is overcome via an approach that is significantly different from a well-known method based on the so-called duality principle. On the other hand, the second aspect requires the establishment of a criterion for the existence of exponential moments of functions of the random time change.
Keywords
Cite
@article{arxiv.2006.10926,
title = {Strong approximation of time-changed stochastic differential equations involving drifts with random and non-random integrators},
author = {Sixian Jin and Kei Kobayashi},
journal= {arXiv preprint arXiv:2006.10926},
year = {2021}
}
Comments
Restriction placed on the dimension in section 5; the second figure updated; minor modifications for clarification purposes made throughout