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We show that if ψ(A) = ψ(B) is satisfied then many properties enjoyed by nonsingular borderings have analogs for singular (or rectangular) borderings as well.. This
We show that the Langevin equation with fractional Brownian mo- tion noise also has a stationary solution and that the decay of its auto-covariance function is like that of a
Under this assumption we prove that the x -component of the Wiener process converges weakly to a Markov process that behaves like a standard diffusion process away from the points
In the case of branching systems we show that the multiple space time scale analysis can be applied even on the level of the historical process , that is, the process encoding the
We show that, given the Poisson process points, almost surely, the chance of surviving to time t is like e − αlog ( 1 k ) t , as t tends to infinity if k, the jump rate of the
This paper discusses the situation that the rate functional has two distinct minimizers, for a simple model described by the pinned Wiener measures with certain densities involving
In the present paper we construct such a Hermitian matrix-valued process, whose entries are sums of Brownian motions and Brownian bridges given independently of each other, that
If we are to use the dual process to obtain information about the joint distribution of the states at sites x and y at a given time, we must study the joint behavior of two
