Conditional gauge theorem for non - local Feynman - Kac transforms
نویسنده
چکیده
Feynman-Kac transforms driven by discontinuous additive functionals are studied in this paper for a large class of Markov processes. General gauge and conditional gauge theorems are established for such transforms. Furthermore, the L2-infinitesimal generator of the Schrödinger semigroup given by a non-local Feynman-Kac transform is determined in terms of its associated bilinear form.
منابع مشابه
On General Perturbations of Symmetric Markov Processes
Let X be a symmetric right process, and let Z = {Zt, t ≥ 0} be a multiplicative functional of X that is the product of a Girsanov transform, a Girsanov transform under time-reversal and a continuous Feynman-Kac transform. In this paper we derive necessary and sufficient conditions for the strong L-continuity of the semigroup {Tt, t ≥ 0} given by Ttf(x) = Ex [Ztf(Xt)], expressed in terms of the ...
متن کاملA non asymptotic variance theorem for unnormalized Feynman-Kac particle models
We present a non asymptotic theorem for interacting particle approximations of unnormalized Feynman-Kac models. We provide an original stochastic analysis based on Feynman-Kac semigroup techniques combined with recently developed coalescent tree-based functional representations of particle block distributions. We present some regularity conditions under which the L2relative error of these weigh...
متن کاملJa n 20 04 Relative Fatou ’ s Theorem for ( − ∆ ) α / 2 - harmonic Functions in Bounded κ - fat Open Set ∗
Recently it was shown in Kim [26] that Fatou's theorem for transient censored α-stable processes in a bounded C 1,1 open set is true. Here we give a probabilistic proof of relative Fatou's theorem for (−∆) α/2-harmonic functions (equivalently for symmetric α-stable processes) in bounded κ-fat open set where α ∈ (0, 2). That is, if u is positive (−∆) α/2-harmonic function in a bounded κ-fat open...
متن کاملFeynman-kac Penalisations of Symmetric Stable Pro- Cesses
In [9], [10], B. Roynette, P. Vallois and M. Yor have studied limit theorems for Wiener processes normalized by some weight processes. In [16], K. Yano, Y. Yano and M. Yor studied the limit theorems for the one-dimensional symmetric stable process normalized by non-negative functions of the local times or by negative (killing) Feynman-Kac functionals. They call the limit theorems for Markov pro...
متن کاملStability of Dirichlet Heat Kernel Estimates for Non-local Operators under Feynman-kac Perturbation
Abstract. In this paper we show that Dirichlet heat kernel estimates for a class of (not necessarily symmetric) Markov processes are stable under nonlocal Feynman-Kac perturbations. This class of processes includes, among others, (reflected) symmetric stable-like processes in closed d-sets in Rd, killed symmetric stable processes, censored stable processes in C1,1 open sets, as well as stable p...
متن کامل