Seminar on Stochastic Processes, 1989 by Richard F. Bass, Krzysztof Burdzy (auth.), E. Çinlar, K. L.

By Richard F. Bass, Krzysztof Burdzy (auth.), E. Çinlar, K. L. Chung, R. K. Getoor, P. J. Fitzsimmons, R. J. Williams (eds.)

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Wahrscheinlichkeitstheorie verw. , 67 (1984), 1-62. [GStl) R. K. Getoor and J. Steffens. The energy functional, balayage, and capacity. Ann. Inst. Henri Poincare, 23 (1987), 321-357. [GSt2] R. K. Getoor and J. Steffens. More about capacity and excessive measures. Sem. Stoch. , 1987, 135-157. Birkhauser, Boston, 1988. BLUMENTHAL-GETOOR-McKEAN THEOREM 57 [Gll) J. Glover. Representing last exit potentials as potentials of measures. Z. Wahrscheinlichkeitstheorie verw. , 61 (1982), 17-30. [Gl2) J. Glover.

J. FITZSIMMONS. R. K. GETOOR and M. J. ce for the processes (X, T) and tained by killing X (resp. t) at T (resp. it follows that H E &<. The Borel q T). Y, T) ob- Since -algebra 11. of H is the trace of £ on H and so 11. C &e . 2) (extended to BE &e) that (X, T) and (X, T) have the same hitting distributions for sets in 11.. 2]. Y, T) SeX, T) c £e(X). Y). Similarly If B E £e we write TB = E\B. It follows C &e(x). p = P' [exp (-T»). Y, T). = T(B) = P' [exp( -T)] E &e(x). 2), PX(TF < 00) =1 =1 for all x E E (equivalently for all a' E E).

J. 4) Proposition. Let X and (E,E). Suppose that PK(X,,) Then 5 = S. H X and X be right processes with the same state space = FK(X,,) for each x E E and compact K C E. are transient, then the equality 5 = S implies that PB(x,·)=FB(X,,) for all xEE and BEE. Proof. 33]. The converse for transient processes is proved on page 553 of [Fl]. (8t w) identically in t,s,and w. 19}, for example) this entails no loss of generality. We are now prepared to state BGM for transient processes. 5) Theorem. ) for each x E E and BEE.

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