The asymptotic distribution of the bootstrap sample mean depends on the resampling intensity. This paper explores the sensitivity of that distribution against different resampling intensities. It is generally assumed that small resampling sizes make the bootstrap work. However, we will show that...

We consider a collection of linearly interacting diffusions (indexed by a countable space) in a random medium. The diffusion coefficients are the product of a space-time dependent random field (the random medium) and a function depending on the local state. The main focus of the present work is...

We consider the following hidden Markov chain problem: estimate the finite-dimensional parameter [theta] in the equation when we observe discrete data Xi/n at times i=0,...,n from the diffusion . The processes (Wt)t[set membership, variant][0,1] and (Bt)t[set membership, variant][0,1] are two...

Let d[greater-or-equal, slanted]2, and let be an i.i.d. family of non-negative random variables with common distribution F. Let N(n) be the maximum value of [summation operator]v[set membership, variant][xi]Xv over all connected subsets [xi] of of size n which contain the origin. This model of...

Longtime behavior for the occupation time of a super-Brownian motion with immigration governed by the trajectory of another super-Brownian motion is considered. Central limit theorems are obtained for dimensions d[greater-or-equal, slanted]3 that lead to some Gaussian random fields: for...

We consider the elementary divisors and determinant of a uniformly distributed nxn random matrix with entries in the ring of integers of an arbitrary local field. We show that the sequence of elementary divisors is in a simple bijective correspondence with a Markov chain on the non-negative...

We consider the question of robustness of the optimal nonlinear filter when the signal process X and the observation noise are possibly correlated. The signal X and observations Y are given by a SDE where the coefficients can depend on the entire past. Using results on pathwise solutions of...

We derive by a constructive method the hydrodynamic behavior of attractive processes with irreducible jumps and product invariant measures. Our approach relies on (i) explicit construction of Riemann solutions without assuming convexity, which may lead to contact discontinuities and (ii) a...

Convergence of stochastic processes with jumps to diffusion processes is investigated in the case when the limit process has discontinuous coefficients. An example is given in which the diffusion approximation of a queueing model yields a diffusion process with discontinuous diffusion and drift...

We prove a result of existence and uniqueness of solutions to forward-backward stochastic differential equations, with non-degeneracy of the diffusion matrix and boundedness of the coefficients as functions of x as main assumptions. This result is proved in two steps. The first part studies the...