Open Access
Translator Disclaimer
July, 1986 On the Rate at Which a Homogeneous Diffusion Approaches a Limit, an Application of Large Deviation Theory to Certain Stochastic Integrals
Daniel W. Stroock
Ann. Probab. 14(3): 840-859 (July, 1986). DOI: 10.1214/aop/1176992441

Abstract

Let $X(T)$ be the solution to a stochastic differential equation whose coefficients are homogeneous of degree 1 (e.g., a linear S.D.E.). Under mild conditions, it is shown that limits like $\lim_{T\rightarrow\infty} \frac{1}{T} \log P(|X(T)|/|X(0)| \geq R)$ exist and a formula is provided for their computation. The techniques developed apply to a broad class of situations besides the one treated here.

Citation

Download Citation

Daniel W. Stroock. "On the Rate at Which a Homogeneous Diffusion Approaches a Limit, an Application of Large Deviation Theory to Certain Stochastic Integrals." Ann. Probab. 14 (3) 840 - 859, July, 1986. https://doi.org/10.1214/aop/1176992441

Information

Published: July, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0604.60076
MathSciNet: MR841587
Digital Object Identifier: 10.1214/aop/1176992441

Subjects:
Primary: 60J60
Secondary: 60F10 , 60H05

Keywords: diffusion , large deviations

Rights: Copyright © 1986 Institute of Mathematical Statistics

JOURNAL ARTICLE
20 PAGES


SHARE
Vol.14 • No. 3 • July, 1986
Back to Top