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To under- stand why the corresponding statement of Theorem 1.1 could fail for directed graphs we connect the Laplacian for a directed graph with the Laplacian for a
He studies martingales that take self-adjoint matrix values, and he shows that the maximum eigenvalue of the martingale satisfies a tail bound similar to Freedman’s inequality..
In Section 2 we first review the decomposition of the size-biased Galton-Watson tree along the distin- guished line of descent of a particle chosen purely at random and give a
In particular, when the Markov process in question is a diffusion, we obtain the integral test corresponding to a law of the iterated logarithm due to
We consider a system of nonlinear partial differential equations with stochastic dynamical boundary conditions that arises in models of neurophysiology for the diffusion of
[1] study discretization schemes for stochastic differential equations with multivalued drift coefficients; Martinez and Talay [4] study discretization schemes for diffusion
More precisely it was shown that, when the Markov transition matrix on each branch satisfies the Kesten-Stigum bound, the phylogeny can be reconstructed in polynomial time
We can therefore invert the foregoing Laplace transform with respect to ν and we get the formula (4.9) corresponding to the case of the maximum functional... However, the