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that the open sets in the topology correspond to the ideals in the preorder: a topology on X having k open sets, corresponds to a preorder with k ideals and vice versa..
Compared with standard applications of the second moment method in related problems, the analysis here requires the control of second order terms in the large deviation
Brownian motion, fine topology, local maxima, optional
In the second example, although the family of conditioned laws are tight in the Martin topology, they possess multiple limit points so that weak convergence fails altogether..
So, using the martingale property of M we see that N is a local martingale. The equivalence between i) and ii) in the above proposition corresponds to a well known
The aim of this paper is to prove that the open set Γ is con- nected using the ideas introduced in the proof of the one-dimensional case, and assuming weak regularity assumptions on
Furthermore, the criterion applies to two important classes of branching random walks and implies that the critical branching random walk is transient resp.. dies
In particular, on the space P (ID) of laws of stochastic processes with trajectories in ID the topology S induces a sequential topology for which both the direct and the
