Multilevel Monte Carlo for Stochastic Differential Equations with Small Noise

The multilevel Monte-Carlo Method for stochastic differential equations driven by jump-diffusion processes

In this article we discuss the multilevel Monte Carlo method for stochastic differential equations driven by jump-diffusion processes. We show that for a reasonable jump intensity the multilevel Monte Carlo method for jump-diffusions reduces the computational complexity compared to the standard Monte Carlo method significantly for a given mean square accuracy. Carrying out numerical experiments...

Stabilized Numerical Methods for Stochastic Differential Equations driven by Diffusion and Jump-Diffusion Processes

Stochastic models that account for sudden, unforeseeable events play a crucial role in many different fields such as finance, economics, biology, chemistry, physics and so on. That kind of stochastic problems can be modeled by stochastic differential equations driven by jumpdiffusion processes. In addition, there are situations, where a stochastic model is based on stochastic differential equat...

Multilevel Monte Carlo for stochastic differential equations with additive fractional noise

Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation.

This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to intro...

Numerical Methods in the Weak Sense for Stochastic Differential Equations with Small Noise

We propose a new approach to constructing weak numerical methods for finding solutions to stochastic systems with small noise. For these methods we prove an error estimate in terms of products hiεj (h is a time increment, ε is a small parameter). We derive various efficient weak schemes for systems with small noise and study the Talay–Tubaro expansion of their global error. An efficient approac...