Randomized derivative-free Milstein algorithm for efficient approximation of solutions of SDEs under noisy information

Abstract

We deal with pointwise approximation of solutions of scalar stochastic differential equations in the presence of informational noise about underlying drift and diffusion coefficients. We define a randomized derivative-free version of Milstein algorithm ${\bar{\mathcal{A}}}_n^{df-RM}$ and investigate its error. We also study lower bounds on the error of an arbitrary algorithm. It turns out that in some case the scheme ${\bar{\mathcal{A}}}_n^{df-RM}$ is the optimal one. Finally, in order to test the algorithm ${\bar{\mathcal{A}}}_n^{df-RM}$ in practice, we report performed numerical experiments.

References in corpus (2)

• A randomized Milstein method for stochastic differential equations with non-differentiable drift coefficients
• Optimal approximation of stochastic integrals in analytic noise model

Cited by in corpus (4)

• Complexity of randomized algorithms for underdamped Langevin dynamics
• Efficient approximation of SDEs driven by countably dimensional Wiener process and Poisson random measure
• Randomized Runge-Kutta method -- stability and convergence under inexact information
• Euler scheme for approximation of solution of nonlinear ODEs under inexact information