In this paper, we study the homeomorphic property of solutions of multi-dimensional stochastic differential equations with non-Lipschitz coefficients.

Existence, uniqueness and continuity of mild solutions are established for stochastic linear functional differential equations in an appropriate Hilbert space which is particularly suitable for stability analysis. An attempt is made to obtain some infinite dimensional stochastic extensions of...

With the help of a general methodology of asymptotic expansions for mixing processes, we obtain the Edgeworth expansion for log-returns of a stock price process in Barndorff-Nielsen and Shephard's stochastic volatility model, in which the latent volatility process is described by a stationary...

We extend the domain of the divergence operator [delta] for Gaussian processes in the sense of the calculus of variations. As an example, we discuss the case of the fractional Brownian motion with Hurst parameter in defined on a finite time interval. If this process does not belong to the domain...

We prove that the number Z(N) of level crossings of a two-parameter simple random walk in its first NxN steps is almost surely N3/2+o(1) as N--[infinity]. The main ingredient is a strong approximation of Z(N) by the crossing local time of a Brownian sheet. Our result provides a useful algorithm...

Stationary random closed sets [Xi] in are considered whose realizations belong to the extended convex ring. A new approach is proposed to joint estimation of the specific intrinsic volumes of [Xi], including the specific Euler-Poincaré characteristic , the specific surface area , and the volume...

We consider a system of stochastic partial differential equations modeling heat conduction in a non-linear medium. We show global existence of solutions for the system in Sobolev spaces of low regularity, including spaces with norm beneath the energy norm. For the special case of thermal...

In this paper we consider an arbitrary irreducible random walk on , d[greater-or-equal, slanted]1, with i.i.d. increments, together with an arbitrary i.i.d. random scenery. Walk and scenery are assumed to be independent. Random walk in random scenery (RWRS) is the random process where time is...

This paper introduces a three-dimensional object point process--the Bisous model--that can be used as a prior for three-dimensional spatial pattern analysis. Maximization of likelihood or penalized-likelihood functions based on this model requires global optimization techniques, such as the...

We study the super-Brownian motion (Xt) conditioned on the total mass as the continuous limit of a system of branching trajectories which genealogical structure is a Galton-Watson tree conditioned on the number of its vertices. We characterize this process by a martingale problem and give a...