On the Small Time Asymptotics of Diffusion Processes on Path Groups

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Harnack inequality and strong Feller property for stochastic fast-diffusion equations☆ (2007, unknown): “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.”
Harnack and functional inequalities for generalized Mehler semigroups (2003, unknown): “[1,2,4,5,10,13,16,17] and references therein).”
Harnack inequality and applications for stochastic evolution equations with monotone drifts (2008, unknown): “AMS Subject Classification: 60H15; 60J35; 47D07.”
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,”
White Noise Driven SPDEs with Reflection: Strong Feller Properties and Harnack Inequalities (2010, background): “For every non-negative f ∈ L2([0, 1]), the Eq.”