Open AccessRecurrency of an Oscillating Random Walk
Author(s) -
B. A. Rogozin,
Sergey Foss
Publication year - 1978
Publication title -
theory of probability and its applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 32
eISSN - 1095-7219
pISSN - 0040-585X
DOI - 10.1137/1123015
Subject(s) - random walk , mathematics , markov chain , statistical physics , random variable , joint probability distribution , distribution (mathematics) , statistics , physics , mathematical analysis
X {-g4(t, e)lx-yl+lx-yl-[2(x-y, a(t,x)-a(t, y)) + 2 Iri(t,x)-ri(t, y)l=-Ix-yl-= E (x-y, crj(t,x)-cri(t, y))2-<_0 i=1 by (6). Moreover (assuming that Ka(t, R)>=O) we also have as a consequence of the conditions o,.(zl, R) dzl <-1, (7) and (8) that (lI ds)(K6(R)Ix-ylKs(t'R)o(Ix-yl2)) _-< 2R exp-Kn(s, R) d (K4(t, R)+ Ks(t, R)K6(R)).
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