Skorokhod imbedding via stochastic integrals
Using stochastic comparison to estimate Green's functions
Markov processes and convex minorants
A probabilistic approach to the boundedness of singular integral operators
inequalities for functionals of brownian motion
Stochastic differential equations driven by symmetric stable processes
A stability theorem for elliptic Harnack inequalities
We prove a stability theorem for the elliptic Harnack inequality: if two weighted graphs are equivalent, then the elliptic Harnack inequality holds for harmonic functions with respect to one of the graphs if and only if it holds for harmonic functions with respect to the other graph. As part of the proof, we give a characterization of the elliptic Harnack inequality.
Stochastic calculus and the continuity of local times of Lévy processes
On the martingale problem for super-brownian motion
Intersection Local Times and Tanaka Formulas
The supremum of brownian local times on Hölder curves
Erratum to “The supremum of brownian local times on Hölder curves”
The construction of brownian motion on the Sierpinski carpet
Uniqueness for reflecting brownian motion in lip domains
Symmetric jump processes : localization, heat kernels and convergence
We consider symmetric processes of pure jump type. We prove local estimates on the probability of exiting balls, the Hölder continuity of harmonic functions and of heat kernels, and convergence of a sequence of such processes.
Uniqueness of Brownian motion on Sierpiński carpets
We prove that, up to scalar multiples, there exists only one local regular Dirichlet form on a generalized Sierpi´nski carpet that is invariant with respect to the local symmetries of the carpet. Consequently, for each such fractal the law of Brownian motion is uniquely determined and the Laplacian is well defined.
Extending the Wong-Zakai theorem to reversible Markov processes
We show how to construct a canonical choice of stochastic area for paths of reversible Markov processes satisfying a weak Hölder condition, and hence demonstrate that the sample paths of such processes are rough paths in the sense of Lyons. We further prove that certain polygonal approximations to these paths and their areas converge in -variation norm. As a corollary of this result and standard properties of rough paths, we are able to provide a significant generalization of the classical result...
Uniqueness for the Skorokhod equation with normal reflection in Lipschitz domains.
The measurability of hitting times.
Stochastic differential equations with jumps.
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