Seminar on Stochastic Processes, 1989

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.