In this paper, we consider a uniformly ergodic Markov process (Xn)n[greater-or-equal, slanted]0 valued in a measurable subset E of Rd with the unique invariant measure , where the density f is unknown. We establish the large deviation estimations for the nonparametric kernel density estimator in...

Consider a centered separable Gaussian process Y with a variance function that is regularly varying at infinity with index 2H[set membership, variant](0,2). Let [phi] be a 'drift' function that is strictly increasing, regularly varying at infinity with index [beta]H, and vanishing at the origin....

Relations between harnesses and initial enlargements of the filtration of a Lévy process with its positions at fixed times are investigated.

We prove that the pseudoprocesses governed by heat-type equations of order n[greater-or-equal, slanted]2 have a local time in zero (denoted by ) whose distribution coincides with the folded fundamental solution of a fractional diffusion equation of order 2(n-1)/n, n[greater-or-equal, slanted]2....

Functionals of spatial point process often satisfy a weak spatial dependence condition known as stabilization. We prove general Donsker-Varadhan large deviation principles (LDP) for such functionals and show that the general result can be applied to prove LDPs for various particular functionals,...

We introduce the mathematical theory of the particle systems that interact via permutations, where transition rates are assigned not to the jumps from a site to a site, but to the permutations themselves. These permutation processes can be viewed as the natural generalization of symmetric...

We consider the nearest neighbor asymmetric exclusion process on , in which particles jump with probability p(1) to the right and p(-1) to the left. Let q=p(1)/p(-1) and denote by [nu]q an ergodic component of the reversible Bernoulli product measure which places a particle at x with probability...

We show that the method of Kipnis and Varadhan [Comm. Math. Phys. 104 (1986) 1-19] to construct a Martingale approximation to an additive functional of a stationary ergodic Markov process via the resolvent is universal in the sense that a martingale approximation exists if and only if the...

In this paper, we deal with the real stochastic difference equation , where the sequence (an) is a finite state space Markov chain. By means of the renewal theory, we give a precise description of the situation where the tail of its stationary solution exhibits power law behavior.

Let X= X(t),t[set membership, variant]R+ be an operator stable Lévy process in Rd with exponent B, where B is an invertible linear operator on Rd. We determine the Hausdorff dimension and the packing dimension of the range X([0,1]) in terms of the real parts of the eigenvalues of B.