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| LARGE DEVIATIONS FOR SYMMETRIC DIFFUSION PROCESSES |
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Citation： |
Qian Zhongmin（钱忠民）,Wei Guoqiang（魏国强）.LARGE DEVIATIONS FOR SYMMETRIC DIFFUSION PROCESSES[J].Chinese Annals of Mathematics B,1992,13(4):430~439 |
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Net amount： 827 |
Authors： |
Qian Zhongmin（钱忠民）; Wei Guoqiang（魏国强） |
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| Abstract： |
Let a(x)=(a_ij(x)) be a uniformly continuous,symmetric and matrix-valued function satisfying uniformly elliptic condition,p(t,x,y) be the transition density function of the diffusion process assciated with the Dirichlet space $(\varepsilon,H_0^1(R^d))$,where $\[\varepsilon (u,v) = \frac{1}{2}\int\limits_{{R^d}} {\sum\limits_{i,j}^d {\frac{{\partial u(x)}}{{\partial {x_i}}}} } \frac{{\partial v(x)}}{{\partial {x_j}}}{a_{ij}}(x)dx\]$.Then by using the sharpened Aronson's estimates established by D.W.Stroock,it is shown that $\[\mathop {\lim }\limits_{t \to 0} 2t\ln p(t,x,y) = - {d^2}(x,y)\] $ .Moreover,it is proved that P_y^s has large deviation property with rate function $\[I(w) = \frac{1}{2}\int\limits_0^1 { < \dot w(t),{a^{ - 1}}} (w(t)),\dot w(t) > dt\] $ as $s\rightarrow 0$ and $y\rightarrow x$,where P_y^s denotes the diffusion measure family associated with the Dirichlet form $\[(\varepsilon ,H_0^1({R^d}))\] $. |
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