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The last term in the horizontal part of the reduced geodesic spray is related to the curvature of the horizontal distribution, at least in the case when M is a Riemannian manifold
Reflecting Brownian motion can be constructed as a strong Markov process not only on a domain with smooth or Lipschitz boundary with H¨ older cusps (see Lions and Sznitman [10],
(2007) use ingenious arguments based on ideas from differential games to show that a bounded convex planar domain cannot support any shy couplings of reflected Brownian motions if
We first show that Brownian motions conditioned not to intersect have a good chance of being reasonably far apart, and conclude that the corresponding simple walks are also far
Indeed, it seems that case (a) should give us the right picture: in the limit, in between large events lineages perform Brownian motions on the torus of sidelength 1 due to
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..
Keywords Wiener space, Sobolev space, Stochastic integral, Fractional Brownian Motion, Itˆ o’s formula.. AMS Subject Classification (1991)
Keywords: Malliavin calculus, Clark-Ocone formula, Brownian local time, Knight theorem, central limit theorem, Tanaka
