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Celebratio Mathematica

Elton Pei Hsu


Bibliography

[1]P. Hsu: “Prob­ab­il­ist­ic ap­proach to the Neu­mann prob­lem,” Comm. Pure Ap­pl. Math. 38 : 4 (1985), pp. 445–​472. MR 792399 Zbl 0587.​60077

[2]P. Hsu and P. March: “The lim­it­ing angle of cer­tain Rieman­ni­an Browni­an mo­tions,” Comm. Pure Ap­pl. Math. 38 : 6 (1985), pp. 755–​768. MR 812346 Zbl 0615.​58044

[3]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

[4]P. Hsu: “On ex­cur­sions of re­flect­ing Browni­an mo­tion,” Trans. Amer. Math. Soc. 296 : 1 (1986), pp. 239–​264. MR 837810 Zbl 0602.​60070

[5]P. Hsu: “Browni­an exit dis­tri­bu­tion of a ball,” pp. 108–​116 in Sem­in­ar on stochast­ic pro­cesses, 1985 (Gaines­ville, FL, 1985). Pro­gr. Probab. Stat­ist. 12. Birkhäuser (Bo­ston, MA), 1986. MR 896739 Zbl 0629.​60091

[6]P. Hsu: “On the Pois­son ker­nel for the Neu­mann prob­lem of Schrödinger op­er­at­ors,” J. Lon­don Math. Soc. (2) 36 : 2 (1987), pp. 370–​384. MR 906154 Zbl 0624.​60070

[7]P. Hsu: “Branch­ing Browni­an mo­tion and the Di­rich­let prob­lem of a non­lin­ear equa­tion,” pp. 71–​83 in Sem­in­ar on stochast­ic pro­cesses, 1986 (Char­lottes­ville, VA, 1986). Pro­gr. Probab. Stat­ist. 13. Birkhäuser (Bo­ston, MA), 1987. MR 902427 Zbl 0619.​60078

[8]P. Hsu and P. March: “Browni­an ex­cur­sions from ex­tremes,” pp. 502–​507 in Sémin­aire de prob­ab­ilités, XXII. Lec­ture Notes in Math. 1321. Spring­er (Ber­lin), 1988. MR 960545

[9]P. Hsu: “Browni­an mo­tion and Rieman­ni­an geo­metry,” pp. 95–​104 in Geo­metry of ran­dom mo­tion (Ithaca, NY, 1987). Con­temp. Math. 73. Amer. Math. Soc. (Provid­ence, RI), 1988. MR 954633 Zbl 0658.​58044

[10]P. Hsu: “Sur la fonc­tion \( \Theta \) d’une variété rieman­niene à bord,” C. R. Acad. Sci. Par­is Sér. I Math. 309 : 7 (1989), pp. 507–​510. MR 1055469

[11]P. Hsu: “Asymp­tot­ic be­ha­vi­or of solu­tions of ob­lique de­riv­at­ive bound­ary value prob­lems,” Michigan Math. J. 36 : 2 (1989), pp. 221–​244. MR 1000526 Zbl 0692.​58038

[12]P. Hsu: “Heat semig­roup on a com­plete Rieman­ni­an man­i­fold,” Ann. Probab. 17 : 3 (1989), pp. 1248–​1254. MR 1009455 Zbl 0694.​58043

[13]M. Cran­ston, P. Hsu, and P. March: “Smooth­ness of the con­vex hull of planar Browni­an mo­tion,” Ann. Probab. 17 : 1 (1989), pp. 144–​150. MR 972777 Zbl 0678.​60073

[14]P. Hsu: “Short-time asymp­tot­ics of the heat ker­nel on a con­cave bound­ary,” SIAM J. Math. Anal. 20 : 5 (1989), pp. 1109–​1127. MR 1009349 Zbl 0685.​58035

[15]P. Hsu: “Heat ker­nel on non­com­plete man­i­folds,” In­di­ana Univ. Math. J. 39 : 2 (1990), pp. 431–​442. MR 1089046 Zbl 0689.​58033

[16]P. Hsu: “Prob­ab­il­ist­ic meth­ods in dif­fer­en­tial geo­metry,” pp. 123–​134 in Sem­in­ar on stochast­ic pro­cesses, 1989 (San Diego, CA, 1989). Pro­gr. Probab. 18. Birkhäuser (Bo­ston, MA), 1990. MR 1042344 Zbl 0698.​58051

[17]R. F. Bass and P. Hsu: “The se­mi­martin­gale struc­ture of re­flect­ing Browni­an mo­tion,” Proc. Amer. Math. Soc. 108 : 4 (1990), pp. 1007–​1010. MR 1007487 Zbl 0694.​60075

[18]P. Hsu: “Browni­an bridges on Rieman­ni­an man­i­folds,” Probab. The­ory Re­lated Fields 84 : 1 (1990), pp. 103–​118. MR 1027823 Zbl 0698.​58052

[19]R. F. Bass and P. Hsu: “Some po­ten­tial the­ory for re­flect­ing Browni­an mo­tion in Hölder and Lipschitz do­mains,” Ann. Probab. 19 : 2 (1991), pp. 486–​508. MR 1106272 Zbl 0732.​60090

[20]P. Hsu: “On the \( \Theta \)-func­tion of a Rieman­ni­an man­i­fold with bound­ary,” Trans. Amer. Math. Soc. 333 : 2 (1992), pp. 643–​671. MR 1055808 Zbl 0764.​58033

[21]E. P. Hsu: “A class of sin­gu­lar con­tinu­ous func­tions,” Elem. Math. 47 : 4 (1992), pp. 169–​172. MR 1200332 Zbl 0799.​26007

[22]P. Hsu and W. S. Kend­all: “Lim­it­ing angle of Browni­an mo­tion in cer­tain two-di­men­sion­al Cartan–Hadam­ard man­i­folds,” Ann. Fac. Sci. Toulouse Math. (6) 1 : 2 (1992), pp. 169–​186. MR 1202070 Zbl 0770.​60074

[23]E. P. Hsu: “A do­main mono­ton­icity prop­erty of the Neu­mann heat ker­nel,” Osaka J. Math. 31 : 1 (1994), pp. 215–​223. MR 1262798

[24]E. P. Hsu: “Flows and quasi-in­vari­ance of the Wien­er meas­ure on path spaces,” pp. 265–​279 in Stochast­ic ana­lys­is (Ithaca, NY, 1993). Proc. Sym­pos. Pure Math. 57. Amer. Math. Soc. (Provid­ence, RI), 1995. MR 1335476 Zbl 0830.​58035

[25]E. P. Hsu: “Inégalités de So­bolev log­ar­ithmiques sur un es­pace de chemins,” C. R. Acad. Sci. Par­is Sér. I Math. 320 : 8 (1995), pp. 1009–​1012. MR 1328728 Zbl 0826.​46023

[26]E. P. Hsu: “Quasi-in­vari­ance of the Wien­er meas­ure on the path space over a com­pact Rieman­ni­an man­i­fold,” J. Funct. Anal. 134 : 2 (1995), pp. 417–​450. MR 1363807 Zbl 0847.​58082

[27]E. P. Hsu: “On the prin­ciple of not feel­ing the bound­ary for dif­fu­sion pro­cesses,” J. Lon­don Math. Soc. (2) 51 : 2 (1995), pp. 373–​382. MR 1325580 Zbl 0822.​58053

[28]E. P. Hsu: “In­teg­ra­tion by parts in loop spaces,” Math. Ann. 309 : 2 (1997), pp. 331–​339. MR 1474195 Zbl 0899.​58008

[29]E. P. Hsu: “Log­ar­ithmic So­bolev in­equal­it­ies on path spaces over Rieman­ni­an man­i­folds,” Comm. Math. Phys. 189 : 1 (1997), pp. 9–​16. MR 1478528 Zbl 0892.​58083

[30]E. P. Hsu: “Stochast­ic loc­al Gauss–Bon­net–Chern the­or­em,” J. The­or­et. Probab. 10 : 4 (1997), pp. 819–​834. MR 1481649 Zbl 0892.​58086

[31]E. P. Hsu: “Log­ar­ithmic So­bolev in­equal­it­ies on path spaces,” pp. 168–​181 in New trends in stochast­ic ana­lys­is (Char­ing­worth, 1994). World Sci. Publ., 1997. MR 1654360

[32]M. Capi­taine, E. P. Hsu, and M. Le­doux: “Mar­tin­gale rep­res­ent­a­tion and a simple proof of log­ar­ithmic So­bolev in­equal­it­ies on path spaces,” Elec­tron. Comm. Probab. 2 (1997), pp. 71–​81. MR 1484557 Zbl 0890.​60045

[33]J. Chen and E. P. Hsu: “Gradi­ent es­tim­ates for har­mon­ic func­tions on man­i­folds with Lipschitz met­rics,” Canad. J. Math. 50 : 6 (1998), pp. 1163–​1175. MR 1657771 Zbl 0972.​58010

[34]Prob­ab­il­ity the­ory and ap­plic­a­tions (Prin­ceton, NJ, June 23–Ju­ly 13, 1996). Edi­ted by E. P. Hsu and S. R. S. Varadhan. IAS/Park City Math­em­at­ics Series 6. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1999. MR 1678306 Zbl 0932.​60005 book

[35]E. P. Hsu: “Ana­lys­is on path and loop spaces,” pp. 277–​347 in Prob­ab­il­ity the­ory and ap­plic­a­tions (Prin­ceton, NJ, 1996). IAS/Park City Math. Ser. 6. Amer. Math. Soc. (Provid­ence, RI), 1999. MR 1678311 Zbl 1069.​60500

[36]E. P. Hsu: “Es­tim­ates of de­riv­at­ives of the heat ker­nel on a com­pact Rieman­ni­an man­i­fold,” Proc. Amer. Math. Soc. 127 : 12 (1999), pp. 3739–​3744. MR 1618694 Zbl 0948.​58025

[37]R. F. Bass and E. P. Hsu: “Path­wise unique­ness for re­flect­ing Browni­an mo­tion in Eu­c­lidean do­mains,” Probab. The­ory Re­lated Fields 117 : 2 (2000), pp. 183–​200. MR 1771660 Zbl 0957.​60070

[38]E. P. Hsu: “Quasi-in­vari­ance of the Wien­er meas­ure on path spaces: non­com­pact case,” J. Funct. Anal. 193 : 2 (2002), pp. 278–​290. MR 1929503 Zbl 1015.​58014

[39]E. P. Hsu: Stochast­ic ana­lys­is on man­i­folds. Gradu­ate Stud­ies in Math­em­at­ics 38. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2002. MR 1882015 Zbl 0994.​58019

[40]E. P. Hsu: “Mul­ti­plic­at­ive func­tion­al for the heat equa­tion on man­i­folds with bound­ary,” Michigan Math. J. 50 : 2 (2002), pp. 351–​367. MR 1914069 Zbl 1037.​58024

[41]E. P. Hsu: “Browni­an mo­tion and Di­rich­let prob­lems at in­fin­ity,” Ann. Probab. 31 : 3 (2003), pp. 1305–​1319. MR 1988474 Zbl 1054.​58027

[42]E. P. Hsu: “Char­ac­ter­iz­a­tion of Browni­an mo­tion on man­i­folds through in­teg­ra­tion by parts,” pp. 195–​208 in Stein’s meth­od and ap­plic­a­tions. Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. 5. Singa­pore Univ. Press (Singa­pore), 2005. MR 2205337

[43]Stochast­ic ana­lys­is and par­tial dif­fer­en­tial equa­tions (North­west­ern Uni­versity, Evan­ston, IL, 2004–2005). Edi­ted by G.-Q. Chen, E. Hsu, and M. Pin­sky. Con­tem­por­ary Math­em­at­ics 429. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2007. MR 2391524

[44]E. P. Hsu: “Heat equa­tions on man­i­folds and Bis­mut’s for­mula,” pp. 121–​130 in Stochast­ic ana­lys­is and par­tial dif­fer­en­tial equa­tions. Con­temp. Math. 429. Amer. Math. Soc. (Provid­ence, RI), 2007. MR 2391533 Zbl 1129.​58013

[45]K. L. Chung: Se­lec­ted works of Kai Lai Chung. Edi­ted by F. Ait­Sah­lia, E. Hsu, and R. Wil­li­ams. World Sci­entif­ic (Hack­en­sack, NJ), 2008. MR 2841270 Zbl 1165.​60302 book

[46]A. Grig­or’yan and E. Hsu: “Volume growth and es­cape rate of Browni­an mo­tion on a Cartan–Hadam­ard man­i­fold,” pp. 209–​225 in So­bolev spaces in math­em­at­ics. II. Int. Math. Ser. (N. Y.) 9. Spring­er (New York), 2009. MR 2484627

[47]E. P. Hsu and C. Ouyang: “Quasi-in­vari­ance of the Wien­er meas­ure on the path space over a com­plete Rieman­ni­an man­i­fold,” J. Funct. Anal. 257 : 5 (2009), pp. 1379–​1395. MR 2541273 Zbl 1173.​58015

[48]E. P. Hsu and G. Qin: “Volume growth and es­cape rate of Browni­an mo­tion on a com­plete Rieman­ni­an man­i­fold,” Ann. Probab. 38 : 4 (2010), pp. 1570–​1582. MR 2663637 Zbl 1200.​58022