An Introduction to Chaos in Nonequilibrium Statistical by J. R. Dorfman

00 For the other inequality, define the stopping time iB = inf{t ::: 0 : At ~ B}. 38 Part I. t A,B,CCS. 14) gives liminf pA(Au n D u----+oo *- 0)::: 00 and then n -+ lim pA(TB(n) < oo)pD(TB(n) < n----+oo *- 0). 00 and 00). 13), pA(TB < 00) ::: aA for all A C S and all finite B C S, and this completes the proof of one direction. 11) holds for all A. 9). ) = A;Y}) lim P(A: t-+oo n B *- 0 for some s ::: t) ::: aAaB. ) ::: aAaB. ) ::: aA. Remark. 13) is independent of x.

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