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January 2000 Large deviation of diffusion processes with discontinuous drift and their occupation times
Tzuu-Shuh Chiang, Shuenn-Jyi Sheu
Ann. Probab. 28(1): 140-165 (January 2000). DOI: 10.1214/aop/1019160115

Abstract

For the system of $d$-dim stochastic differential equations,

dX^{\varepsilon} (t) = b(X^{\varepsilon}(t)) dt + \varepsilon dW(t), \quad t \in [0, 1]

X^{\varepsilon} (0) = x^0 \in R^d

where $b$ is smooth except possibly along the hyperplane $x_1 = 0$, we shall consider the large deviation principle for the lawof the solution diffusion process and its occupation time as $\varepsilon\rightarrow0$. In other words, we consider $P(\|X^\varepsilon-\varphi\|<\delta,\|u^{\varepsilon}-\psi\|\<\delta)$ where $u^\varepsilon(t)$ and $\psi(t)$ are the occupation times of $X^\varepsilon$ and $\varphi$ in the positive half space $\{x\in R^d: x_1>0\}$, respectively. As a consequence, an unified approach of the lower level large deviation principle for the law of $X^\varepsilon(\cdot)$ can be obtained.

Citation

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Tzuu-Shuh Chiang. Shuenn-Jyi Sheu. "Large deviation of diffusion processes with discontinuous drift and their occupation times." Ann. Probab. 28 (1) 140 - 165, January 2000. https://doi.org/10.1214/aop/1019160115

Information

Published: January 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.60065
MathSciNet: MR1756001
Digital Object Identifier: 10.1214/aop/1019160115

Subjects:
Primary: 60J10
Secondary: 60J05

Keywords: Cameron –Martin –Girsanov formula , large deviation principle , Local time , Ventcel–Friedlin theory

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 1 • January 2000
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