Strong approximation of particular one-dimensional diffusions
Abstract
This paper develops a new technique for the path approximation of one-dimensional stochastic processes, more precisely the Brownian motion and families of stochastic differential equations sharply linked to the Brownian motion (usually known as L and G-classes). We are interested here in the ε-strong approximation. We propose an explicit and easy to implement procedure that constructs jointly, the sequences of exit times and corresponding exit positions of some well chosen domains. The main results control the number of steps to cover a fixed time interval and the convergence theorems for our scheme. We combine results on Brownian exit times from time-depending domains (one-dimensional heat balls) and classical renewal theory. Numerical examples and issues are also described in order to complete the theoretical results.
Keywords
Brownian motion
linear diffusion
path simulation
Strong approximation
Strong approximation path simulation Brownian motion linear diffusion. 2010 AMS subject classifications: primary 65C05; secondary 60J60 60J65 60G17
Brownian motion
linear diffusion. 2010 AMS subject classifications: primary 65C05; secondary 60J60
60J65
60G17
Domains
Probability [math.PR]
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Origin : Files produced by the author(s)
Origin : Files produced by the author(s)