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The 1991 Seminar on Stochastic Processes was held at the University of California, Los Angeles, from March 23 through March 25, 1991. This was the eleventh in a series of annual meetings which provide researchers with the opportunity to discuss current work on stochastic processes in an informal and enjoyable atmosphere. Previous seminars were held at Northwestern University, Princeton University, the University of Florida, the University of Virginia, the University of California, San Diego, and the University of British Columbia. Following the successful format of previous years there were five invited lectures. These were given by M. Barlow, G. Lawler, P. March, D. Stroock, M. Talagrand. The enthusiasm and interest of the participants created a lively and stimulating atmosphere for the seminar. Some of the topics discussed are represented by the articles in this volume. P. J. Fitzsimmons T. M. Liggett S. C. Port Los Angeles, 1991 In Memory of Steven Orey M. CRANSTON The mathematical community has lost a cherished colleague with the passing of Steven Orey. This unique and thoughtful man has left those who knew him with many pleasant memories. He has also left us with important contributions in the development of the theory of Markov processes. As a friend and former student, I wish to take this chance to recall to those who know and introduce to those who do not a portion of his lifework.
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The 1991 Seminar on Stochastic Processes was held at the University of California, Los Angeles, from March 23 through March 25, 1991. This was the eleventh in a series of annual meetings which provide researchers with the opportunity to discuss current work on stochastic processes in an informal and enjoyable atmosphere. Previous seminars were held at Northwestern University, Princeton University, the University of Florida, the University of Virginia, the University of California, San Diego, and the University of British Columbia. Following the successful format of previous years there were five invited lectures. These were given by M. Barlow, G. Lawler, P. March, D. Stroock, M. Talagrand. The enthusiasm and interest of the participants created a lively and stimulating atmosphere for the seminar. Some of the topics discussed are represented by the articles in this volume. P. J. Fitzsimmons T. M. Liggett S. C. Port Los Angeles, 1991 In Memory of Steven Orey M. CRANSTON The mathematical community has lost a cherished colleague with the passing of Steven Orey. This unique and thoughtful man has left those who knew him with many pleasant memories. He has also left us with important contributions in the development of the theory of Markov processes. As a friend and former student, I wish to take this chance to recall to those who know and introduce to those who do not a portion of his lifework.
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The1989SeminaronStochasticProcesseswasheldattheUniversityof CaliforniaatSanDiegoonMarch30,31andApril1,Hl89. Thiswastheninth inanannualseriesofmeetingswhichprovideresearcherswiththeopportunity todiscusscurrentworkonstochasticprocessesinaninformalandenjoyableat- mosphere. PreviousseminarswereheldatPrincetonUniversity,Northwestern University,theUniversityofFloridaandtheUniversityofVirginia. Theseminar hasgrownovertheyears,withatotalofseventy-fiveparticipantsin1989. Fol- lowingthesuccessfulformatofpreviousyears,therewerefiveinvitedlectures, deliveredby K. L. Chung,D. Dawson, R. Durrett,N. IkedaandT. Lyons,with theremainderoftimebeingdevotedtostructured,butlessformal,discussionson currentworkandproblems. Severalsmallergroupsalsoheldworkshopsessions onspecifictopicssuchas:mper-processes,diffusionsonfractalsandHarnack inequalities. Theparticipant. s'interestandenthusiasmcreatedalivelyandstim- ulatingcnvironmentfortheseminar. Asampleoftheresearchdiscussedthereis containedinthisvolume. Thc1989SeminarwasmadepossiblebythesupportoftheNationalScience Foundation,theNationalSecurityAgencyandtheUniversityofCaliforniaatSan Diego.\Yeextendourthankstothem,andtothepublishcrBirkhauserBoston, fortheirsupportandencouragemcnt. Finally,thanksgotoLynn\,yilliamsforher cheerfulassistancewiththeseminarorganizationandproductionofthisvolume. P. J. Fitzsimmons R. J. Williams LaJolla,1989 LISTOFPARTICIPANTS P. Arzberger M. Emery E. Perkins J. Pitman B. Atkinson S. N. Evans L. Pitt J. Azema N. Falkner M. Bachman P. Fitzsimmons A. O. Pittenger Z. Pop-Stojanovic M. Barlow R. K. Getoor R. Bass J. Glover S. Port C. Bezuidenhout H. Heyer P. Protter R. Blumenthal K. Hoffmann K. M. Rao G. Brosamler J. Horowitz J. Rosen C. Burdzy P. Hsu T. Salisbury D. Burkholder N. Ikeda M. J. Sharpe H. Cai O. Kallenberg C. T. Shih R. Carmona F. Knight A. Sznitman W. Chen-Masters Y. Kwon M. Taksar K. L. Chung T. Kurtz L. Taylor E. Cinlar T. Liggett S. J. Taylor M. Cranston T. Lyons G. Terdik R. Dalang P. March E. Toby R. DanteDeBlassie M. Marcus R. Tribe R. Darling P. McGill J. Walsh D. Dawson T. Mountford J. Watkins J. Deuschel B. Oksendal S. Weinryb N. Dinculeanu V. Papanicolaou R. Williams R. Durrett R. Pemantle Z. Zhao E. B. Dynkin M. Penrose W. Zheng TABLEOFCONTENTS R. F. BASS Aprobabilisticproofoftheboundary 1 and K.BURDZY Harnackprinciple J. -D. DEUSCHEL LogarithmicSobolevinequalitiesof 17 symmetricdiffusions S. N. EVANS RescalingthevacancyofaBoolean coverageprocess 23 TheBlumenthal-Getoor-McKean P. J. FITZSIMMONS, R. K. GETOOR Theoremrevisited 35 andM. J. SHARPE P. J. FITZSIMMONS Localtimes,occupationtimes,andthe Lebesguemeasureoftherangeofa andS. C.