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(f) A possible reason why sub-fractional Brownian motion is the limit in the non-branching model with deterministic θ (Remark 2.3(a)) and in the branching model (Theorem 2.4(a)) is
The boundary dimension of B [0 , 1] is the Hausdorff dimension of the “frontier” of Brownian motion, where the frontier of planar Brownian motion is t he boundary of the un-
The answer (Theorem 2 ) is a mixed process of the type described in [ 7 ], more precisely a Brownian particle (profile) which is reborn (copied) in the interior of the region D
On the scaling limit we can describe the behavior of the total current through the origin up to a given time when the jump rate has macroscopic fluctuations in space (as well as
In the paper [STW], it was shown that “a Brownian motion reflected on an independent time-reversed Brownian motion is again a Brownian motion” combining the fact that the
coordinate systems this problem is reduced to the ǫ-covering time of the two-dimensional (flat) torus by a (standard) Brownian motion. In this paper we deal with manifolds of
the time reversed process is a drifted fractional Brownian motion, which continuously extends the one obtained in the theory of time reversal of Brownian diffusions when H = 1/2..
The expression just obtained for the distribution of coalescing Brownian motions is closely related to the formula for the transition density of the interlaced Brownian motions given
