## The Annals of Probability

### On the Rate at Which a Homogeneous Diffusion Approaches a Limit, an Application of Large Deviation Theory to Certain Stochastic Integrals

Daniel W. Stroock

#### 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.

#### Article information

Source
Ann. Probab., Volume 14, Number 3 (1986), 840-859.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176992441

Digital Object Identifier
doi:10.1214/aop/1176992441

Mathematical Reviews number (MathSciNet)
MR841587

Zentralblatt MATH identifier
0604.60076

JSTOR