In this paper, we state a large deviation principle (LDP) and sharp LDP for maximum likelihood estimators of drift coefficients of generalized squared radial Ornstein-Uhlenbeck processes. For that purpose, we present an LDP in a class of non-steep cases, where the Gärtner-Ellis theorem cannot...

We consider the exponential decay rate of the stationary tail probabilities of reflected Brownian motion X in the N-dimensional orthant having drift b, covariance matrix A, and constraint matrix D. Suppose that the Skorokhod or reflection mapping associated with the matrix D is well-defined and...

A growing body of recent works have been devoted to the study of the favorite points of various concrete Markov processes. We contribute to this subject by showing that for a large class of recurrent strongly symmetric Markov processes, singletons are polar for the most visited site(s).

Bivariate occupation measure dimension is a new dimension for multidimensional random processes. This dimension is given by the asymptotic behavior of its bivariate occupation measure. Firstly, we compare this dimension with the Hausdorff dimension. Secondly, we study relations between these...

Let (B,[short parallel]·[short parallel]) be a real separable Banach space of dimension 1[less-than-or-equals, slant]d[less-than-or-equals, slant][infinity], and assume X,X1,X2,... are i.i.d. B valued random vectors with law and mean . Nummelin's conditional weak law of large numbers...

Let Xt be a continuous local martingale satisfying X0=0 and K1q(t)[less-than-or-equals, slant]<X>t[less-than-or-equals, slant]K2q(t) a.s. for a nondecreasing function q with constants K1 and K2. Define for a Borel function and Mt*=sup0[less-than-or-equals, slant]s[less-than-or-equals, slant]t Ms....</x>

We prove the smoothness of a diffusion coefficient with respect to the density of particles for a non-gradient type model. This fact gives a complete proof of the hydrodynamic equation for lattice gas reversible under Bernoulli measures.

We show that sufficient conditions in terms of moments for cumulative processes (additive functionals of regenerative processes) to satisfy the central limit theorem and the weak law of large numbers established in Glynn and Whitt (Stochastic Process. Appl. 47 (1993) 299-314) are also necessary,...

This paper studies bounded-velocity control of a Brownian motion when discretionary stopping, or 'leaving', is allowed. The goal is to choose a control law and a stopping time in order to minimize the expected sum of a running and a termination cost, when both costs increase as a function of...

We derive a Hamilton-Jacobi equation for the macroscopic evolution of a class of growth models. For the definition of our growth models, we need a uniformly positive bounded continuous function which is uniformly Lipshitz in its last argument, and a nonnegative function with v(0)=0. The space of...