Differential Calculus and Integration by Parts on Poisson Space
Differential Calculus and Integration by Parts on Poisson Space
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DOI：
10.1007/978-94-011-7976-8_5
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发表时间：
1990
期刊：
影响因子：
--
通讯作者：
E. Carlen;É. Pardoux
中科院分区：
文献类型：
--
作者：
E. Carlen;É. Pardoux
我们定义了一个梯度算子的随机变量上定义的“标准泊松空间”（样本空间的路径，有单位的跳跃，是恒定的跳跃之间）。一个“分部积分”公式表明，该算子的伴随扩展了通常的泊松随机积分。证明了一个与几何测度论的余面积公式密切相关的Malliavin演算型结果。
We define a gradient operator on random variables defined on the “standard Poisson space” (the sample space of paths which have unit jumps and are constant between their jumps). An “integration by parts” formula shows that the adjoint of that operator extends the usual Poisson stochastic integral. We prove a “Malliavin calculus” type of result, which is closely related to the co-area formula of geometric measure theory.