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Martin boundary of random walks in convex cones
TLDR
In this paper, the asymptotic behavior of the Green function for zero-drift random walks confined to multidimensional convex cones has been studied, and it has been shown that there is a unique positive discrete harmonic function for these processes up to a multiplicative constant.Abstract:
We determine the asymptotic behavior of the Green function for zero-drift random walks confined to multidimensional convex cones. As a consequence, we prove that there is a unique positive discrete harmonic function for these processes (up to a multiplicative constant); in other words, the Martin boundary reduces to a singleton.read more
Citations
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Principles Of Random Walk
TL;DR: The principles of random walk is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.
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Constructing discrete harmonic functions in wedges
TL;DR: In this article, a systematic construction of signed harmonic functions for discrete Laplacian operators with Dirichlet conditions in the quarter plane was proposed, and it was shown that the set of harmonic functions is an algebra generated by a single element.
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Harmonic Functions of Random Walks in a Semigroup via Ladder Heights
TL;DR: In this article, the convergence of the sequence of ratios for a random walk on a countable group killed upon the time of the first exit from some semigroup with an identity element was investigated.
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Boundary behavior of random walks in cones
Kilian Raschel,Pierre Tarrago +1 more
TL;DR: In this paper, the authors studied the asymptotic behavior of zero-drift random walks confined to multidimensional convex cones, when the endpoint is close to the boundary.
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Martin boundary of a killed non-centered random walk in a general cone
TL;DR: In this article, the authors investigated the Martin boundary for a non-centered random walk on a convex cone with a vertex at the first exit from the first edge of the cone.
References
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David Gilbarg,Neil S. Trudinger +1 more
TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
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Piero Bassanini,Alan R. Elcrat +1 more
TL;DR: In this paper, a class of partial differential equations that generalize and are represented by Laplace's equation was studied. And the authors used the notation D i u, D ij u for partial derivatives with respect to x i and x i, x j and the summation convention on repeated indices.
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Daniel Revuz,Marc Yor +1 more
TL;DR: In this article, the authors present a comprehensive survey of the literature on limit theorems in distribution in function spaces, including Girsanov's Theorem, Bessel Processes, and Ray-Knight Theorem.
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Nonintersecting paths, pfaffians, and plane partitions
TL;DR: Gessel and Viennot as discussed by the authors showed that one may use pfaffiants to enumerate configurations of nonintersecting paths in which the initial and/or terminal vertices of the paths are allowed to vary over specified regions of the digraph.
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