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⋆ Since we did not manage to prove this assertion, we studied the gaps between consec- utive elements of En and showed that it is sufficient to establish that there are almost as
We verify in some cases convergence of scaling limits of these models to a pair of super-Brownian motions interacting through their collision local times, constructed by Evans
The behaviour of the horizontal projection of the random walk is less obvious: in Sections 3, 4 and 5 we prove that the expected values of the horizontal distance, of its
We prove that the Hausdorff dimension of the frontier equals 2(1 − α ) where α is an exponent for Brownian motion called the two-sided disconnection exponent.. In particular, using
We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices.. This random walk, already known to be transient, has
Merkl and Rolles (see [14]) studied the recurrence of the original reinforced random walk, the so-called linearly bond-reinforced random walk, on two-dimensional graphs.. Sellke
In this section we prove the existence of a minimal stopping time which solves the Skorokhod embedding problem for random walk, and make some simple observations which show that
We prove here (by showing convergence of Chen’s series) that linear stochastic differential equa- tions driven by analytic fractional Brownian motion [6, 7] with arbitrary Hurst index
