On the Poisson equation and diffusion approximation 3
E. Pardoux, A. Yu. Veretennikov
Abstract
We study the Poisson equation Lu+f=0 in Rd, where L is the infinitesimal generator of a diffusion process. In this paper, we allow the second-order part of the generator L to be degenerate, provided a local condition of Doeblin type is satisfied, so that, if we also assume a condition on the drift which implies recurrence, the diffusion process is ergodic. The equation is understood in a weak sense. Our results are then applied to diffusion approximation.
Create a lesson
Related papers
Sandpile avalanches in two dimensions are finite
Ahmed Bou-Rabee
Markov Chain Convergence in Kernel-Induced Geometry
Oleksii Kachaiev, Luc Brogat-Motte, Silvia Villa et al.
Interacting Stochastic Systems with Agent-Based Sampling and Connection-Based Reinforcement
Yogesh Dahiya, Gursharn Kaur, Neeraja Sahasrabudhe
Dimension-free Markov--Bernstein-type inequality for R2-valued polynomials
Egor Kosov
Initialization-Dependent Solution Selection by the Euler-Maruyama Scheme for a Degenerate SDE
Akihiro Tanaka
Statistical inference for rough Burgers-type stochastic partial differential equations
Simon Chony Acosta Christian Olivera Ciprian Tudor