@Article{IJNAM-16-6,
author = {Tambue, Antoine and Mukam, Jean, Daniel},
title = {Strong Convergence and Stability of the Semi-Tamed and Tamed Euler Schemes for Stochastic Differential Equations with Jumps under Non-Global Lipschitz Condition},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2019},
volume = {16},
number = {6},
pages = {847--872},
abstract = {<p style="text-align: justify;">We consider the explicit numerical approximations of stochastic differential equations
(SDEs) driven by Brownian process and Poisson jump. It is well known that under non-global
Lipschitz condition, Euler Explicit method fails to converge strongly to the exact solution of such
SDEs without jumps, while implicit Euler method converges but requires much computational
efforts. We investigate the strong convergence, the linear and nonlinear exponential stabilities
of tamed Euler and semi-tamed methods for stochastic differential equation driven by Brownian
process and Poisson jumps, both in compensated and non compensated forms. We prove that
under non-global Lipschitz condition and superlinearly growing drift term, these schemes converge
strongly with the standard one-half order. Numerical simulations to sustain the theoretical results
are provided.</p>},
issn = {2617-8710},
doi = {https://doi.org/2019-IJNAM-13257},
url = {https://global-sci.com/article/83087/strong-convergence-and-stability-of-the-semi-tamed-and-tamed-euler-schemes-for-stochastic-differential-equations-with-jumps-under-non-global-lipschitz-condition}
}