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We prove a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof uses a coupling argument based on the observation that the random walk eventually gets trapped inside the union of space–time cones contained in the infection clusters generated by single infections. In the case where the local drifts of the random walk are smaller than the speed at which infection clusters grow, the random walk...
Regression and scale invariant -test procedures are developed for detection of structural changes in linear regression model. Their limit properties are studied under the null hypothesis.
We study the fluctuations around non degenerate attractors
of the empirical measure under mean field Gibbs measures.
We prove that a mild change of the densities
of these measures does not affect the central limit theorems.
We apply this result to generalize the assumptions
of [3] and [12] on the densities of the Gibbs measures to
get precise Laplace estimates.
In this paper, we study the stability of the solutions of Backward Stochastic Differential Equations (BSDE for short) with an almost surely
finite random terminal time. More precisely, we are going to show that if (Wn) is a sequence of scaled random walks or a sequence of
martingales that converges to a Brownian motion W and if is a sequence of stopping times that converges to a stopping time
τ, then the solution of the BSDE driven by Wn with random terminal time converges to the solution...
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