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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],
Key words: Discounted optimal stopping problem, finite horizon, geometric Brownian motion, maximum process, parabolic free-boundary problem, smooth fit, normal reflection, a
The proof is largely based on the Costin-Lebowitz- Soshnikov argument and the asymptotic estimates for the expectation and variance of the number of eigenvalues in an interval..
(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
Key words: random fields, Gaussian processes, fractional Brownian motion, fractal mea- sures, self–similar measures, small deviations, Kolmogorov numbers, metric entropy,
Key words: Brownian sheet, sectorial local nondeterminism, image, Salem sets, multiple points, Hausdorff dimension, packing dimension.. AMS 2000 Subject Classification: Primary
[7] and Evans [8] on the convex hull of planar Brownian path on the unit time interval (recall e.g. that the convex hull is a C 1 curve and that the set of times in [0 , 1] at which
We consider global geometric properties of a codimension one manifold embedded in Euclidean space, as it evolves under an isotropic and volume preserving Brownian flow
