Mixing and convergence rates for a family of Markov processes approximating SDEs
نویسنده
چکیده
We study a class of Markov processes of the type Xn+1,h = Xn,h+ F (Xn,h)h + √ h ξn+1, where F : Rd → Rd is a bounded continuous function, (ξn) are i.i.d. random variables with zero mean, and t = nh understood as “macro-time”. Such processes are approximations to the SDE, dXt = F (Xt) dt + dWt. Upper estimates for β-mixing and convergence rates to invariant measure are established under certain assumptions on smoothness of F , the density of ξn and some recurrence conditions. The estimates are analogous to those for the limiting SDE.
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