Titlebook: Seminar on Stochastic Processes, 1986; E. Çinlar,K. L. Chung,J. Glover Book 1987 Birkhäuser Boston 1987 Markov process.hitting time.stocha

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Measures That Are Translation Invariant In One Coordinate,s due to Dynkin.) Obviously any σ-finite measure is Σ-finite. It is well known that the Fubini theorem is valid for Σ-finite measures, although most text books state it only for σ-finite measures. See, for example, Theorem 7.8a in [2] for the precise statement of what we shall mean by the Fubini the

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Correction,ensated Poisson processes (Theorem 2.4). The principal hypothesis was H3: all martingales are strict. At the end (Theorem 2.9) we asserted a converse to the effect that strictness is necessary for the representation. Unfortunately, the proof has a gap and the assertion is false. The following is a c

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Book 1987eries of meetings which provide opportunities for researchers to discuss current work in stochastic processes in an informal atmosphere. Previous seminars were held at Northwestern University, Evanston and the University of Florida, Gainesville. The participants‘ enthusiasm and interest have resulte

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Correction,y optional T<∞, it would follow that P.(T)∈ Z. (strictness implies Z. = Z., [1,p.119]). However, let T be the minimum of the first jump times of P. and P.. Then the set {P.(T)-P.(T-) = l} is in σ{Z.} but not in σ{Z.}. The converse fails. The same applies to the “Final Remark” of [2], which must be deleted.

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On the Identification of Markov Processes by the Distribution of Hitting Times,e (E,.). Let Δ ε E be a cemetery point used to render the resolvents of X and Y Markovian. Recall that Δ is a trap for X and for Y; the . of X (resp. Y) is then ζ = inf{t: X. = Δ}(resp. n = inf{t: Y. = Δ}). For B ε .,let T(B) = inf{t>0: X.εB}, S(B) = inf{t>0: Y.εB}. Recall that X, for example, is . provided its potential kernel U is proper.