We consider the combined effects of homogenization and large deviations in a stochastic differential equation. We show that there are three regimes, depending on the relative rates at which the small viscosity parameter and the homogenization parameter tend to zero. We prove some...

Consider the functional graph of a random mapping from an n-element set into itself. Then the number of nodes in the strata of this graph can be viewed as stochastic process. Using a generating function approach it is shown that a suitable normalization of this process converges weakly to local...

We consider nearest-neighbor, additive, spin systems on , and show that changing the flip rates at a finite number of sites does not affect survival of the process. We also extend this result to the case of the biased voter model on .

We study existence and continuity of self-intersection local time (SILT) for a Gaussian -valued process which arises as a high-density fluctuation limit of a particle system in where the particle motion switches back and forth between symmetric stable processes of indices [alpha]1 and [alpha]2...

An investor starting with initial wealth z00 would like to achieve a total wealth a where az0 before going bankrupt. The strategy is to allocate his wealth between a chosen risky asset and a bank account. The amount invested in the risky asset is given by an Itô process with infinitesimal...

Suppose is a sequence of random variables such that the probability law of Yn/n satisfies the large deviation principle and suppose . Let T(A)=inf{n: Yn[set membership, variant]A} be the first passage time and, to obtain a suitable scaling, let T[var epsilon](A)=[var epsilon]inf{n: Yn[set...

We consider the filtering problem for partially observable stochastic processes solutions to systems of stochastic difference equations. In the first part of the paper we shall present a simple constructive method to obtain finite dimensional filters in discrete time. Then, applying some...

An arbitrage opportunity is constructed in a frictionless stock market when price processes have continuous sample paths of bounded -variation with .

Let M be a normal martingale (i.e. <M, M> (t) = t), we decompose the product of two multiple stochastic integrals (with respect to M) In(f)Im(g) as a sum of n [logical and] m terms Hk. Hk is equal to the integral over k+ of the function t -- In+m-2k(hk(t,.)), with respect to the k-tensor product of...</m,>

We present an accurate description for the location of maximum of d-dimensional Brownian motion. In case d = 1, this is a well-known theorem of Csáki et al. (1987a). We also deduce, as application, a version of the iterated logarithm law for the favourite site of transient Brownian motion.