## Translation invariant regenerative sets and subprocesses of Markov processes |

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a-field a,n)-generated a,n)-process absolutely continuous Applying Lemma backward transition function compact support conditional independence conditionally independent Consider construct continuous function continuous with respect converges weakly countable number covering process defined Denote discrete equal equivalent exists a.e. finite dimensional distributions following lemma Formula Fubini theorem function f function on TXT given by 1.5 hence II)-generated set II)-process implies independent increments invariant regenerative sets Lebesgue measure M(uu Markov measure measurable spaces one-dimensional distributions P{teM P{zt probability measure process for w(s),P process w(s),P process with independent prove R-lim g(r random set random variable Renewal Theory right side right-continuous satisfies sequence of measures stationary Markov process stationary process Stochastic Processes stopping strong Markov property subject to 1.2 Suppose t.i. set Theorem 2.2 theory transition probabilities TRANSLATION INVARIANT REGENERATIVE two-dimensional distributions virtue of Lemma w-lim weak limit