We introduce a stochastic process based on nonhomogeneous Poisson processes and urn processes which can be reinforced to produce a mixture of semi-Markov processes. By working with the notion of exchangeable blocks within the process, we present a Bayesian nonparametric framework for handling...

The aim of this work is to show how to homogenize a semilinear parabolic second-order partial differential equation, whose coefficients are periodic functions of the space variable, and are perturbed by an ergodic diffusion process, the nonlinear term being highly oscillatory. Our homogenized...

We consider a Langevin dynamics scheme for a d-dimensional Ising model with a disordered external magnetic field and establish that the averaged law of the empirical process obeys a large deviation principle (LDP), according to a good rate functional having a unique minimiser Q[infinity]. The...

Let M be a finite-dimensional smooth-oriented paracompact manifold and [zeta]k, 0[less-than-or-equals, slant]k[less-than-or-equals, slant]d, be a family of complete smooth vector fields on M so that the Brownian flow associated with exists globally. We prove that any volume form [mu] on M is...

We study a singular diffusion on Euclidean space which is characterized by the solution of a classical Itô stochastic differential equation in which the diffusion coefficient is not necessarily of full rank. Our motivation is in earlier results of Basak (J. Multivariate Anal. 39 (1991) 44) and...

This paper discusses the asymptotic behavior of Koul's minimum distance estimators of the regression parameter vector in linear regression models with long memory moving average errors, when the design variables are known constants. It is observed that all these estimators are asymptotically...

We give a new proof of the well-known fact that the pinned Wiener measure on a Lie group is quasi-invariant under right multiplication by finite energy paths. The main technique we use is the time reversal. This approach is different from what B. Driver used to prove quasi-invariance for the...

A new characterization of excessive functions for arbitrary one-dimensional regular diffusion processes is provided, using the notion of concavity. It is shown that excessivity is equivalent to concavity in some suitable generalized sense. This permits a characterization of the value function of...

This paper discusses the consistency and limiting distributions of a class of M-estimators in two-phase random design linear regression models where the regression function is discontinuous at the change-point with a fixed jump size. The consistency rate of an M-estimator for the change-point...

We consider a system of stochastic equations which models the population dynamics of a prey-predator type. We show that the distributions of the solutions of this system are absolutely continuous. We analyse long-time behaviour of densities of the distributions of the solutions. We prove that...