A parameter estimation problem is considered for a stochastic evolution equation on a compact smooth manifold. Specifically, we concentrate on asymptotic properties of spectral estimates, i.e. estimates based on finite number of spatial Fourier coefficients of the solution. Under certain...

We study the asymptotic properties of the integral functionals of solutions of Ito stochastic equations and jump processes with a finite set of values. The limit theorem of weak convergence of measures and the large deviation principle are the main results in this paper.

For one-dimensional simple random walk in a general i.i.d. scenery and its limiting process, we construct a coupling with explicit rate of approximation, extending a recent result for Gaussian sceneries due to Khoshnevisan and Lewis. Furthermore, we explicitly identify the constant in the law of...

We give some probabilistic conditions based on coupling for a functional of a Poisson point process to be differentiable in the intensity [lambda] of this process in a neighborhood of the origin. These conditions are exemplified on various queueing theory problems, and compared with other...

Motivated by applications in option pricing theory (Peskir, 1997b), (Research Report No. 386, Dept. Theoret. Statist. Aarhus, 19 pp.) we formulate and solve the following problem. Given a standard Brownian motion B=(Bt)t[greater-or-equal, slanted]0 and a centered probability measure [mu] on...

We study the tail asymptotics of the r.v. X(T) where {X(t)} is a stochastic process with a linear drift and satisfying some regularity conditions like a central limit theorem and a large deviations principle, and T is an independent r.v. with a subexponential distribution. We find that the tail...

A nonlinear pure-jump Markov process is associated with a singular Kac equation. This process is the unique solution in law for a nonclassical stochastic differential equation. Its law is approximated by simulable stochastic particle systems, with rates of convergence. An effective numerical...

probes are necessary to compute the maximum of a simple symmetric random walk with n steps, in which c appears under the form of a triple integral. In this paper we prove that (log n/log p-log q)+o(log n) probes are necessary to compute the maximum of a simple asymmetric random walk with n...

Two limit theorems on asymptotic behaviors of some processes related to some queueing systems are investigated. In the first result (Theorem 1), sticky diffusions appear as limit processes for queues with vacations. In the second result (Theorem 2), limiting behavior of occupation times and...