Short Time Asymptotics of a Certain Infinite Dimensional Diffusion Process

By S. Aida, Hiroshi Kawabi. 2001

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Harnack inequality and heat kernel estimates on manifolds with curvature unbounded below (2006, background): “This inequality has been applied and further developed to the study of functional inequalities (see [1,22,27,29]), heat kernel estimates (see [4,10]), higher order eigenvalues (see [11,28,30]), transportation cost inequalities (see [5]), and short time behavior of transition probabilities (see [2,3,”
Harnack inequality and applications for stochastic evolution equations with monotone drifts (2008, methodology): “[31, 33, 26, 27] for applications to contractivity properties and functional inequalities; [2, 1 , 14] for applications to short time behaviors of infinite-dimensional diffusions; and [5, 12] for applications to the transportation-cost inequality and heat kernel estimates.”
On the Small Time Asymptotics of Diffusion Processes on Path Groups (2002, methodology): “The following is our main theorem in this section which is an improvement of the lower estimate in [ 3 ].”
Harnack inequality and strong Feller property for stochastic fast-diffusion equations☆ (2007, methodology): “The advantage of this approach is that it avoids the assumption on curvature lower bounds used in previous articles (see [ 2 , 3, 7, 15, 16]), which is very hard to verify in the framework of non-linear SPDEs.”