An adaptive Euler-Maruyama scheme for stochastic differential equations with discontinuous drift and its convergence analysis
Provides a convergent numerical method for a class of SDEs with irregular coefficients, which is important for applications in finance, physics, and biology.
The paper develops an adaptive Euler-Maruyama scheme for SDEs with discontinuous drift and degenerate diffusion, achieving strong convergence order 1/2 (up to log terms) relative to average computational cost.
We study the strong approximation of stochastic differential equations with discontinuous drift coefficients and (possibly) degenerate diffusion coefficients. To account for the discontinuity of the drift coefficient we construct an adaptive step sizing strategy for the explicit Euler-Maruyama scheme. As a result, we obtain a numerical method which has -- up to logarithmic terms -- strong convergence order $1/2$ with respect to the average computational cost. We support our theoretical findings with several numerical examples.