Martin Capacity for Markov Chains
نویسندگان
چکیده
منابع مشابه
Martin Capacity for Markov Chains
The probability that a transient Markov chain, or a Brownian path, will ever visit a given set Λ, is classically estimated using the capacity of Λ with respect to the Green kernel G(x, y). We show that replacing the Green kernel by the Martin kernel G(x, y)/G(0, y) yields improved estimates, which are exact up to a factor of 2. These estimates are applied to random walks on lattices, and also t...
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Kakutani (1944) discovered that a compact set IR is hit with positive probability by a d-dimensional Brownian motion (d 3) if and only if has positive Newtonian capacity. When capacity criteria were transferred to the discrete setting (by Ito and Mckean (1960) and Lamperti (1963)) it was in the form of a \Wiener Test" (c.f. Corollary 2.4). This kind of summability condition is quite e ective in...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1995
ISSN: 0091-1798
DOI: 10.1214/aop/1176988187