Stochastic integration and differential equations
Stochastic integration and differential equations
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DOI：
10.1007/978-3-662-10061-5
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发表时间：
1990
期刊：
影响因子：
--
通讯作者：
P. Protter
中科院分区：
文献类型：
--
作者：
P. Protter
扩散可以被认为是一个具有连续路径的强马尔可夫过程（在n中）。在Itô的布朗运动随机积分理论发展之前，研究扩散的主要方法是研究它们的过渡半群。这相当于研究它们的半群的无穷小生成，即偏微分算子。因此，Feller对扩散的研究（例如）实际上是对偏微分方程的研究，受到扩散的启发。
Adiffusioncan be thought of as a strong Markov process (in ℝn) with continuous paths. Before the development of Itô’s theory of stochastic integration for Brownian motion, the primary method of studying diffusions was to study their transition semigroups. This was equivalent to studying the infinitesimal generators of their semigroups, which are partial differential operators. Thus Feller’s investigations of diffusions (for example) were actually investigations of partial differential equations, inspired by diffusions.