On uniformly subelliptic operators and stochastic area
On uniformly subelliptic operators and stochastic area
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关于均匀次椭圆算子和随机区域
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Nicolas Victoir
中科院分区：
文献类型：
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作者：
P. Friz;Nicolas Victoir
设X a是一个生成元为∑i，j∂i(aij∂j·)的马尔可夫过程，其中a是一致椭圆对称矩阵.由于T.Lyons的基础工作，Xa驱动的随机微分方程组可以在“粗路径意义”下求解，即通过使用适当的随机面积过程来路径地求解。我们对该区域的构造推广了Lyons-Stoica和Lejay的前人的工作，是基于与次下沉算子相关的Dirichlet形式。这使得我们能够特别地讨论大偏差和在适当的粗略路径拓扑中的支持描述。作为典型的粗糙路径推论，Freidlin-Wentzell理论和Stroock-Varadhan支持定理对于Xa驱动的随机微分方程仍然有效。
Let X a be a Markov process with generator ∑i,j∂i( aij∂j· ) where a is a uniformly elliptic symmetric matrix. Thanks to the fundamental works of T. Lyons, stochastic differential equations driven by X a can be solved in the “rough path sense”; that is, pathwise by using a suitable stochastic area process. Our construction of the area, which generalizes previous works of Lyons–Stoica and then Lejay, is based on Dirichlet forms associated to subellitpic operators. This enables us in particular to discuss large deviations and support descriptions in suitable rough path topologies. As typical rough path corollary, Freidlin–Wentzell theory and the Stroock–Varadhan support theorem remain valid for stochastic differential equations driven by X a.