Feynman–Kac theorems for generalized diffusions

Feynman–kac Theorems for Generalized Diffusions

We find Feynman–Kac type representation theorems for generalized diffusions. To do this we need to establish existence, uniqueness and regularity results for equations with measure-valued coefficients.

Class of Limit Theorems for Singular Diffusions

Common Fixed-Point Theorems For Generalized Fuzzy Contraction Mapping

In this paper we investigate common xed point theorems for contraction mapping in fuzzy metric space introduced by Gregori and Sapena [V. Gregori, A. Sapena, On xed-point the- orems in fuzzy metric spaces, Fuzzy Sets and Systems, 125 (2002), 245-252].

Donsker Theorems for Diffusions: Necessary and Sufficient Conditions

We consider the empirical process Gt of a one-dimensional diffusion with finite speed measure, indexed by a collection of functions F . By the central limit theorem for diffusions, the finite-dimensional distributions of Gt converge weakly to those of a zero-mean Gaussian random process G. We prove that the weak convergence Gt ⇒ G takes place in l(F) if and only if the limit G exists as a tight...

Quasistationary Theorems for Diffusions in a Bounded Open Set

Let X be the minimal diffusion associated with a uniformly elliptic differential operator L on a bounded subdomain of Rd, with C2 boundary. Under the only assumption that the coefficients of L be Hölder continuous, we prove all the standard quasistationary limit theorems (cf. Markov chain theory). Moreover, we show that the laws of X, conditioned on explosion occuring after time s, converge in ...