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Celebratio Mathematica

Kai Lai Chung

Probability

Brownian motion and potential theory

[1]K. L. Chung, P. Er­dős, and T. Sirao: “On the Lipschitz’s con­di­tion for Browni­an mo­tion,” J. Math. Soc. Ja­pan 11 : 4 (1959), pp. 263–​274. MR 0121873 Zbl 0091.​13301 article

[2]K. L. Chung: “On last exit times,” Illinois J. Math. 4 : 4 (1960), pp. 629–​639. MR 0130715 Zbl 0094.​32102 article

[3]K. L. Chung: “Prob­ab­il­ist­ic ap­proach in po­ten­tial the­ory to the equi­lib­ri­um prob­lem,” Ann. Inst. Four­i­er (Gren­oble) 23 : 3 (1973), pp. 313–​322. MR 0391277 Zbl 0258.​31012 article

[4]K. L. Chung: “Note on last exit de­com­pos­i­tion,” pp. 20–​21 in Sémin­aire de Prob­ab­il­ités VIII (Uni­versité de Stras­bourg, an­née uni­versitaire 1972–1973). Edi­ted by C. Del­larcher­ie, P. Mey­er, and M. Weil. Lec­ture Notes in Math­em­at­ics 381. Spring­er (Ber­lin), 1974. MR 0378117 Zbl 0295.​60056 incollection

[5]K. L. Chung: “An ex­pres­sion for ca­non­ic­al en­trance laws,” pp. 311–​314 in Stochast­ic ana­lys­is: A trib­ute to the memory of Rollo Dav­id­son. Edi­ted by D. G. Kend­all and E. F. Hard­ing. Wiley Series in Prob­ab­il­ity and Stat­ist­ics. Wiley (Lon­don), 1974. MR 0368189 incollection

[6]K. L. Chung: “Re­marks on equi­lib­ri­um po­ten­tial and en­ergy,” pp. xiv, 131–​138 in Col­lec­tion of art­icles ded­ic­ated to Mar­cel Brelot on the oc­ca­sion of his 70th birth­day, published as Ann. Inst. Four­i­er (Gren­oble) 25 : 3–​4 (1975). MR 0405601 Zbl 0338.​31001 incollection

[7]K. L. Chung: “Max­ima in Browni­an ex­cur­sions,” Bull. Amer. Math. Soc. 81 : 4 (July 1975), pp. 742–​745. MR 0373035 Zbl 0325.​60077 article

[8]K. L. Chung: “Ap­prox­im­a­tion of a con­tinu­ous para­met­er Markov chain by dis­crete skel­et­ons,” Bull. Lon­don Math. Soc. 7 : 1 (1975), pp. 71–​76. MR 0388540 Zbl 0301.​60046 article

[9]K. L. Chung: “Ex­cur­sions in Browni­an mo­tion,” Ark. Mat. 14 : 1–​2 (1976), pp. 155–​177. Ded­ic­ated to the Memory of Paul Lévy. MR 0467948 Zbl 0356.​60033 article

[10]K. L. Chung: “Ped­ago­gic notes on the bar­ri­er the­or­em,” pp. 27–​33 in Sémin­aire de prob­ab­il­ités XI (Uni­versité de Stras­bourg, an­née uni­versitaire 1975–1976). Edi­ted by C. Del­lacher­ie, P. A. Mey­er, and M. Weil. Lec­ture Notes in Math­em­at­ics 581. Spring­er (Ber­lin), 1977. MR 0445620 Zbl 0376.​60080 incollection

[11]K. L. Chung and R. K. Getoor: “The con­dens­er prob­lem,” Ann. Prob­ab­il­ity 5 : 1 (February 1977), pp. 82–​86. MR 0428480 Zbl 0381.​60064 article

[12]K. L. Chung: “Cor­rec­tion to: ‘Ped­ago­gic notes on the bar­ri­er the­or­em’,” pp. 739 in Sémin­aire de prob­ab­il­ités XII (Uni­versité de Stras­bourg, an­née uni­versitaire 1976–1977). Lec­ture Notes in Math­em­at­ics 649. Spring­er (Ber­lin), 1978. MR 520034 incollection

[13]K. L. Chung and S. R. S. Varadhan: “Kac func­tion­al and Schrödinger equa­tion,” Stu­dia Math. 68 : 3 (1980), pp. 249–​260. MR 599148 Zbl 0448.​60054 article

[14]K. L. Chung and K. M. Rao: “Sur la théor­ie du po­ten­tiel avec la fonc­tion­nelle de Feyn­man–Kac,” C. R. Acad. Sci. Par­is Sér. A-B 290 : 13 (1980), pp. A629–​A631. MR 572652 Zbl 0439.​31005 article

[15]K. L. Chung and M. Rao: “Equi­lib­ri­um and en­ergy,” Probab. Math. Stat­ist. 1 : 2 (1980), pp. 99–​108. MR 626304 Zbl 0502.​60060 article

[16]K. L. Chung and K. M. Rao: “A new set­ting for po­ten­tial the­ory, I,” Ann. Inst. Four­i­er (Gren­oble) 30 : 3 (1980), pp. 167–​198. MR 597022 Zbl 0424.​31004 article

[17]K. L. Chung: “On stopped Feyn­man–Kac func­tion­als,” pp. 347–​356 in Sémin­aire de prob­ab­il­ités XIV (Par­is, 1978–1979). Edi­ted by J. Azéma and M. Yor. Lec­ture Notes in Math­em­at­ics 784. Spring­er (Ber­lin), 1980. MR 580141 Zbl 0444.​60061 incollection

[18]K. L. Chung and K. M. Rao: “Feyn­man–Kac func­tion­al and the Schrödinger equa­tion,” pp. 1–​29 in Sem­in­ar on stochast­ic pro­cesses, 1981 (North­west­ern Uni­versity, Evan­ston, IL, April 1981). Edi­ted by E. Çin­lar, K. L. Chung, and R. K. Getoor. Pro­gress in Prob­ab­il­ity and Stat­ist­ics 1. Birkhäuser (Bo­ston, MA), 1981. MR 647779 Zbl 0492.​60073 incollection

[19]K. L. Chung: “Browni­an mo­tion on the line, I,” J. Math. Res. Ex­pos­i­tion 1 : 1 (1981), pp. 74–​82. MR 617355 Zbl 0583.​60074 article

[20]K. L. Chung: “A cluster of great for­mu­las,” Acta Math. Acad. Sci. Hun­gar. 39 : 1–​3 (1982), pp. 65–​67. MR 653674 Zbl 0495.​60020 article

[21]K. L. Chung: “Browni­an mo­tion on the line, II,” J. Math. Res. Ex­pos­i­tion 2 : 3 (1982), pp. 87–​98. MR 672218 Zbl 0583.​60075 article

[22]K. L. Chung, R. Dur­rett, and Z. X. Zhao: “Ex­ten­sion of do­mains with fi­nite gauge,” Math. Ann. 264 : 1 (1983), pp. 73–​79. MR 709862 Zbl 0519.​60080 article

[23]K. L. Chung: “An in­equal­ity for bound­ary value prob­lems,” pp. 111–​122 in Sem­in­ar on stochast­ic pro­cesses, 1982 (North­west­ern Uni­versity, Evan­ston, IL, March 1982). Edi­ted by E. Çin­lar, K. L. Chung, and R. K. Getoor. Pro­gress in Prob­ab­il­ity and Stat­ist­ics 5. Birkhäuser (Bo­ston, MA), 1983. MR 733667 Zbl 0528.​60071 incollection

[24]K. L. Chung: “Prop­er­ties of fi­nite gauge with an ap­plic­a­tion to loc­al time,” pp. 16–​24 in Prob­ab­il­ity and math­em­at­ic­al stat­ist­ics: es­says in hon­our of Carl-Gust­av Es­s­een (Uppsala, Sweden, 1983). Edi­ted by A. Gut and L. Holst. Uppsala Uni­versity, 1983. MR 727123 Zbl 0519.​60081 incollection

[25]K. L. Chung and Z. X. Zhao: “Some prob­ab­il­ist­ic res­ults on the Sturm–Li­ouville equa­tion,” J. Sys­tems Sci. Math. Sci. 4 : 4 (1984), pp. 320–​324. MR 820144 Zbl 0591.​60075 article

[26]K. L. Chung: “The life­time of con­di­tion­al Browni­an mo­tion in the plane,” Ann. Inst. H. Poin­caré Probab. Stat­ist. 20 : 4 (1984), pp. 349–​351. MR 771894 Zbl 0573.​60070 article

[27]K. L. Chung, M. Liao, and K. M. Rao: “Du­al­ity un­der a new set­ting,” pp. 23–​38 in Sem­in­ar on stochast­ic pro­cesses, 1983 (Uni­versity of Flor­ida, Gaines­ville, FL, 1983). Edi­ted by E. Çin­lar, K. L. Chung, and R. K. Getoor. Pro­gress in Prob­ab­il­ity and Stat­ist­ics 7. Birkhäuser (Bo­ston, MA), 1984. MR 902410 Zbl 0558.​60056 incollection

[28]K. L. Chung: “Con­di­tion­al gauges,” pp. 17–​22 in Sem­in­ar on stochast­ic pro­cesses, 1983 (Uni­versity of Flor­ida, Gaines­ville, FL, 1983). Edi­ted by E. Çin­lar, K. L. Chung, and R. K. Getoor. Pro­gress in Prob­ab­il­ity and Stat­ist­ics 7. Birkhäuser (Bo­ston, MA), 1984. MR 902409 Zbl 0552.​60073 incollection

[29]K. L. Chung: “The gauge and con­di­tion­al gauge the­or­em,” pp. 496–​503 in Sémin­aire de prob­ab­il­ités XIX (Uni­versité de Stras­bourg, an­née uni­versitaire, 1983–84). Edi­ted by J. Azéma. Lec­ture Notes in Math­em­at­ics 1123. Spring­er (Ber­lin), 1985. MR 889497 Zbl 0561.​60084 incollection

[30]K. L. Chung and Z. X. Zhao: “A simple proof of a new the­or­em on con­di­tion­al Browni­an mo­tion,” Kexue Tong­bao (Chinese) 30 : 5 (1985), pp. 329–​332. MR 803587 article

[31]K. L. Chung: “Prob­ab­il­ist­ic ap­proach to bound­ary value prob­lems for Schrödinger’s equa­tion,” Ex­pos­i­tion. Math. 3 : 2 (1985), pp. 175–​178. MR 816403 Zbl 0577.​60066 article

[32]K. L. Chung and P. Li: “Com­par­is­on of prob­ab­il­ity and ei­gen­value meth­ods for the Schrödinger equa­tion,” pp. 25–​34 in Prob­ab­il­ity, stat­ist­ic­al mech­an­ics, and num­ber the­ory. Edi­ted by G.-C. Rota. Ad­vances in Math­em­at­ics Sup­ple­ment­ary Stud­ies 9. Aca­dem­ic Press (Or­lando, FL), 1986. Volume ded­ic­ated to Mark Kac. MR 875443 Zbl 0608.​60061 incollection

[33]K. L. Chung and P. Hsu: “Gauge the­or­em for the Neu­mann prob­lem,” pp. 63–​70 in Sem­in­ar on stochast­ic pro­cesses, 1984 (North­west­ern Uni­versity, Evan­ston, IL, 1984). Edi­ted by E. Çin­lar, K. L. Chung, and R. K. Getoor. Pro­gress in Prob­ab­il­ity and Stat­ist­ics 9. Birkhäuser (Bo­ston, MA), 1986. MR 896722 Zbl 0585.​60064 incollection

[34]K. L. Chung, P. Li, and R. J. Wil­li­ams: “Com­par­is­on of prob­ab­il­ity and clas­sic­al meth­ods for the Schrödinger equa­tion,” Ex­pos­i­tion. Math. 4 : 3 (1986), pp. 271–​278. MR 880127 Zbl 0623.​60097 article

[35]K. L. Chung: “Notes on the in­homo­gen­eous Schrödinger equa­tion,” pp. 55–​62 in Sem­in­ar on stochast­ic pro­cesses, 1984 (North­west­ern Uni­versity, Evan­ston, IL, 1984). Edi­ted by E. Çin­lar, K. L. Chung, and R. K. Getoor. Pro­gress in Prob­ab­il­ity and Stat­ist­ics 9. Birkhäuser (Bo­ston, MA), 1986. MR 896721 Zbl 0585.​60063 incollection

[36]K. L. Chung: “Re­mark on the con­di­tion­al gauge the­or­em,” pp. 423–​425 in Sémin­aire de Prob­ab­il­ités XX (Uni­versité de Stras­bourg, an­née uni­versitaire 1984/85). Edi­ted by J. Azéma and M. Yor. Lec­ture Notes in Math­em­at­ics 1204. Spring­er (Ber­lin), 1986. MR 942036 incollection

[37]K. L. Chung: “Green’s func­tion for a ball,” pp. 1–​13 in Sem­in­ar on stochast­ic pro­cesses, 1986 (Uni­versity of Vir­gin­ia, Char­lottes­ville, VA, March, 1986). Edi­ted by E. Çin­lar, K. L. Chung, R. K. Getoor, and J. Glover. Pro­gress in Prob­ab­il­ity and Stat­ist­ics 13. Birkhäuser (Bo­ston, MA), 1987. MR 902422 Zbl 0643.​31007 incollection

[38]K. L. Chung and K. M. Rao: “Gen­er­al gauge the­or­em for mul­ti­plic­at­ive func­tion­als,” Trans. Amer. Math. Soc. 306 : 2 (April 1988), pp. 819–​836. MR 933320 Zbl 0647.​60083 article

[39]K. L. Chung: “Prob­ab­il­ity meth­ods in po­ten­tial the­ory,” pp. 42–​54 in Po­ten­tial the­ory — sur­veys and prob­lems (Prague, Ju­ly 19–24, 1987). Edi­ted by J. Král, J. Lukeš, I. Netuka, and J. Veselý. Lec­ture Notes in Math­em­at­ics 1344. Spring­er (Ber­lin), 1988. MR 973880 Zbl 0677.​60085 incollection

[40]K. L. Chung: “Gauge the­or­em for un­boun­ded do­mains,” pp. 87–​98 in Sem­in­ar on stochast­ic pro­cesses, 1988 (Uni­versity of Flor­ida, Gaines­ville, FL, March 3–5, 1988). Edi­ted by E. Çin­lar, K. L. Chung, R. K. Getoor, and J. Glover. Pro­gress in Prob­ab­il­ity 17. Birkhäuser (Bo­ston, MA), 1989. MR 990475 Zbl 0689.​60076 incollection

[41]K. L. Chung: “Greeni­an bounds for Markov pro­cesses,” Po­ten­tial Anal. 1 : 1 (1992), pp. 83–​92. MR 1245226 Zbl 1081.​60543 article