标题： 奥恩斯坦-乌伦贝克桥及其在马尔可夫半群中的应用 显示英文标题

标题： The Ornstein Uhlenbeck Bridge and Applications to Markov Semigroups

摘要： 对于任意的Hilbert空间值的Ornstein-Uhlenbeck过程，我们构造了一个连接起点$x$和属于全测度线性子空间的终点$y$的Ornstein-Uhlenbeck桥。我们还推导了OU桥满足的随机演化方程并研究了其基本性质。然后利用OU桥来研究带有加性噪声的非线性随机演化方程相关的马尔可夫转移半群。我们提供了转移密度的显式公式并研究了其正则性。给定强Feller性质和不变测度的存在性，我们证明了转移半群将$L^p$函数映射为连续函数。我们还证明了转移算子是$q$-求和的，对于某些$q>p>1$而言，特别是Hilbert-Schmidt型。 显示英文摘要

摘要： For an arbitrary Hilbert space-valued Ornstein-Uhlenbeck process we construct the Ornstein-Uhlenbeck Bridge connecting a starting point $x$ and an endpoint $y$ that belongs to a certain linear subspace of full measure. We derive also a stochastic evolution equation satisfied by the OU Bridge and study its basic properties. The OU Bridge is then used to investigate the Markov transition semigroup associated to a nonlinear stochastic evolution equation with additive noise. We provide an explicit formula for the transition density and study its regularity. Given the Strong Feller property and the existence of an invariant measure we show that the transition semigroup maps $L^p$ functions into continuous functions. We also show that transition operators are $q$-summing for some $q>p>1$, in particular of Hilbert-Schmidt type.