Strong invariance principle for singular diffusions

Strong invariance principle for singular di$usions

We study a singular di$usion on Euclidean space which is characterized by the solution of a classical Itô stochastic di$erential equation in which the di$usion coe2cient is not necessarily of full rank. Our motivation is in earlier results of Basak (J. Multivariate Anal. 39 (1991) 44) and Basak and Bhattacharya (Ann. Probab. 20 (1992) 312), who establish su2cient conditions for singular di$usio...

Strong invariance principle for dependent random fields

A strong invariance principle is established for random fields which satisfy dependence conditions more general than positive or negative association. We use the approach of Csörgő and Révész applied recently by Balan to associated random fields. The key step in our proof combines new moment and maximal inequalities, established by the authors for partial sums of multiindexed random variables, ...

A Strong Invariance Principle for Associated Random Fields ? ?

In this paper we generalize Yu’s [Ann. Probab. 24 (1996) 2079–2097] strong invariance principle for associated sequences to the multiparameter case, under the assumption that the covariance coefficient u(n) decays exponentially as n → ∞. The main tools that we use are the following: the Berkes and Morrow [Z. Wahrsch. Verw. Gebiete 57 (1981) 15–37] multi-parameter blocking technique, the Csörgő ...

Class of Limit Theorems for Singular Diffusions

On the Poisson Equation for Singular Diffusions

Pardoux and Veretennikov [2001, Ann. Probab. 29, 1061-1085] establish existence (in the Sobolev sense) and uniqueness of solutions of a Poisson equation for the differential operator of an ergodic diffusion in <D, for which the covariance term is strictly non-degenerate and uniformly bounded. Our goal is to establish a similar solvability result, but for the complementary case of singular diffu...