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Strong order 1 adaptive approximation of jump-diffusion SDEs with discontinuous drift
Verena Schwarz
We present an adaptive approximation scheme for jump-diffusion SDEs with discontinuous drift and (possibly) degenerate diffusion. This transformation-based doubly-adaptive quasi-Mi…
Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift
Paweł Przybyłowicz, Verena Schwarz, Michaela Szölgyenyi
In this note we prove sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift. We study the approximatio…
Randomized Milstein algorithm for approximation of solutions of jump-diffusion SDEs
Paweł Przybyłowicz, Verena Schwarz, Michaela Szölgyenyi
We investigate the error of the randomized Milstein algorithm for solving scalar jump-diffusion stochastic differential equations. We provide a complete error analysis under substa…
A higher order approximation method for jump-diffusion SDEs with discontinuous drift coefficient
Paweł Przybyłowicz, Verena Schwarz, Michaela Szölgyenyi
We present the first higher-order approximation scheme for solutions of jump-diffusion stochastic differential equations with discontinuous drift. For this transformation-based jum…