Strong Feller solutions to SPDE's are strong Feller in the weak topology
نویسندگان
چکیده
منابع مشابه
Regime-switching diffusion processes: strong solutions and strong Feller property
We investigate the existence and uniqueness of strong solutions up to an explosion time for regime-switching diffusion processes in an infinite state space. Instead of concrete conditions on coefficients, our existence and uniqueness result is established under the general assumption that the diffusion in every fixed environment has a unique non-explosive strong solution. Moreover, non-explosio...
متن کاملThe strong Feller property for singular stochastic PDEs
We show that the Markov semigroups generated by a large class of singular stochastic PDEs satisfy the strong Feller property. These include for example the KPZ equation and the dynamical Φ3 model. As a corollary, we prove that the Brownian bridge measure is the unique invariant measure for the KPZ equation with periodic boundary conditions.
متن کامل[hal-00668272, v1] Strong solutions to semilinear SPDEs
Abstract. We study the Cauchy problem for a semilinear stochastic partial differential equation driven by a finite-dimensional Wiener process. In particular, under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives, we consider the equation in the context of power scale generated by a strongly elliptic differential operator. Application of semigroup ar...
متن کاملStrong and Weak Order in Averaging for Spdes
We show an averaging result for a system of stochastic evolution equations of parabolic type with slow and fast time scales. We derive explicit bounds for the approximation error with respect to the small parameter defining the fast time scale. We prove that the slow component of the solution of the system converges towards the solution of the averaged equation with an order of convergence is 1...
متن کاملFeller Processes and Semigroups
For convenience, we can have a look at the list of materials contained in this lecture first. Note here we always consider the time-homogenous Markov processes. • Transition kernels μt, t ≥ 0 ←→ transition operators semigroup Tt, t ≥ 0. • Feller semigroup Tt, t ≥ 0 • Feller processes • existence • every Feller process has a cadlag version • regularization theorem for submartingale • strong Mark...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Studia Mathematica
سال: 2001
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm148-2-2