Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
140 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Modified Euler approximation scheme for stochastic differential equations driven by fractional Brownian motions (1306.1458v2)

Published 6 Jun 2013 in math.PR

Abstract: For a stochastic differential equation driven by a fractional Brownian motion with Hurst parameter $H> \frac12$ it is known that the classical Euler scheme has the rate of convergence $2H-1$. In this paper we introduce a new numerical scheme which is closer to the classical Euler scheme for diffusion processes, in the sense that it has the rate of convergence $2H-\frac12$. In particular, the rate of convergence becomes $\frac 12$ when $H$ is formally set to $\frac 12$ (the rate of Euler scheme for classical Brownian motion). The rate of weak convergence is also deduced for this scheme. The main tools are fractional calculus and Malliavin calculus. We also apply our approach to the classical Euler scheme.

Summary

We haven't generated a summary for this paper yet.