椭球上infinite-dimensional扩散过程转移概率的正性
Positivity of transition probabilities of infinite-dimensional diffusion processes on ellipsoids
摘要：
我们考虑希尔伯特空间中具有常数非退化扩散算子的扩散过程，并证明了在关于漂移的广泛假设下，该过程的转移概率在与扩散算子相关的椭球上是正的.这是转移概率密度的正性的无限维模拟。我们的结果适用于相应的随机偏微分方程的扩散。
英文摘要：
We consider diffusion processes in Hilbert spaces with constant non-degenerate diffusion operators and show that, under broad assumptions on the drift, the transition probabilities of the process are positive on ellipsoids associated with the diffusion operator. This is an infinite-dimensional analogue of positivity of densities of transition probabilities. Our results apply to diffusions corresponding to stochastic partial differential equations.
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