In applications of branching processes, usually it is hard to obtain samples of a large size. Therefore, a bootstrap procedure allowing inference based on a small sample size is very useful. Unfortunately, in the critical branching process with stationary immigration the standard parametric...

This paper proves weak convergence in D of the tail empirical process-the renormalized extreme tail of the empirical process-for a large class of stationary sequences. The conditions needed for convergence are (i) moment restrictions on the amount of clustering of extremes, (ii) restrictions on...

Two types of Gaussian processes, namely the Gaussian field with generalized Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic properties of the spectral densities of these random fields are...

We establish a boundary Harnack principle for a large class of subordinate Brownian motions, including mixtures of symmetric stable processes, in [kappa]-fat open sets (disconnected analogue of John domains). As an application of the boundary Harnack principle, we identify the Martin boundary...

We study the problem of parameter estimation for generalized Ornstein-Uhlenbeck processes driven by [alpha]-stable noises, observed at discrete time instants. Least squares method is used to obtain an asymptotically consistent estimator. The strong consistency and the rate of convergence of the...

This paper studies drawdown and drawup processes in a general diffusion model. The main result is a formula for the joint distribution of the running minimum and the running maximum of the process stopped at the time of the first drop of size a. As a consequence, we obtain the probabilities that...

A large deviation principle is established for the Poisson-Dirichlet distribution when the mutation rate [theta] converges to zero. The rate function is identified explicitly, and takes on finite values only on states that have finite number of alleles. This result is then applied to the study...

Necessary and sufficient conditions for the existence of a strictly stationary solution of the equations defining a general Lévy-driven continuous-parameter ARMA process with index set are determined. Under these conditions the solution is shown to be unique and an explicit expression is given...

A gradient-entropy inequality is established for elliptic diffusion semigroups on arbitrary complete Riemannian manifolds. As applications, a global Harnack inequality with power and a heat kernel estimate are derived.

This work is concerned with a class of jump-diffusion processes with state-dependent switching. First, the existence and uniqueness of the solution of a system of stochastic integro-differential equations are obtained with the aid of successive construction methods. Next, the non-explosiveness...