## The Annals of Probability

### Large Deviations for a Class of Anticipating Stochastic Differential Equations

#### Abstract

Consider the family of perturbed stochastic differential equations on $\mathbb{R}^d$, $X^\varepsilon_t = X^\varepsilon_0 + \sqrt{\varepsilon} \int^t_0\sigma(X^\varepsilon_s)\circ dW_s + \int^t_0 b(X^\varepsilon_s) ds,$ $\varepsilon > 0$, defined on the canonical space associated with the standard $k$-dimensional Wiener process $W$. We assume that $\{X^\varepsilon_0, \varepsilon > 0\}$ is a family of random vectors not necessarily adapted and that the stochastic integral is a generalized Stratonovich integral. In this paper we prove large deviations estimates for the laws of $\{X^\varepsilon_., \varepsilon > 0\}$, under some hypotheses on the family of initial conditions $\{X^\varepsilon_0, \varepsilon > 0\}$.

#### Article information

Source
Ann. Probab., Volume 20, Number 4 (1992), 1902-1931.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176989535

Digital Object Identifier
doi:10.1214/aop/1176989535

Mathematical Reviews number (MathSciNet)
MR1188048

Zentralblatt MATH identifier
0769.60053

JSTOR