Markov chain approximations to non-symmetric diffusions with bounded coefficients
نویسندگان
چکیده
We consider a certain class of non-symmetric Markov chains and obtain heat kernel bounds and parabolic Harnack inequalities. Using the heat kernel estimates, we establish a sufficient condition for the family of Markov chains to converge to non-symmetric diffusions. As an application, we approximate non-symmetric diffusions in divergence form with bounded coefficients by non-symmetric Markov chains. This extends the results by Stroock-Zheng ([SZ]) to the non-symmetric divergence forms.
منابع مشابه
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 ...
متن کاملThe non-locality of Markov chain approximations to two-dimensional diffusions
In this short paper, we consider discrete-time Markov chains on lattices as approximations to continuous-time diffusion processes. The approximations can be interpreted as finite difference schemes for the generator of the process. We derive conditions on the diffusion coefficients which permit transition probabilities to match locally first and second moments. We derive a novel formula which e...
متن کاملDrift Transformations of Symmetric Diffusions, and Duality
Starting with a symmetric Markov diffusion process X (with symmetry measure m and L(m) infinitesimal generator A) and a suitable core C for the Dirichlet form of X, we describe a class of derivations defined on C. Associated with each such derivation B is a drift transformation of X, obtained through Girsanov’s theorem. The transformed process X is typically non-symmetric, but we are able to sh...
متن کاملMarkov chain approximations for symmetric jump processes
Markov chain approximations of symmetric jump processes are investigated. Tightness results and a central limit theorem are established. Moreover, given the generator of a symmetric jump process with state space Rd the approximating Markov chains are constructed explicitly. As a byproduct we obtain a definition of the Sobolev space Hα/2(Rd), α ∈ (0, 2), that is equivalent to the standard one.
متن کاملConvergence rates of Markov chain approximation methods for controlled diffusions with stopping
This work is concerned with rates of convergence of numerical methods using Markov chain approximation for controlled diffusions with stopping (the first exit time from a bounded region). In lieu of considering the associated finite difference schemes for Hamilton-Jacobi-Bellman (HJB) equations, a purely probabilistic approach is used. There is an added difficulty due to the boundary condition,...
متن کامل