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Celebratio Mathematica

Ruth J. Williams


Bibliography

[1]R. J. Wil­li­ams: “Suf­fi­cient con­di­tions for Nash equi­lib­ria in \( N \)-per­son games over re­flex­ive Banach spaces,” J. Op­tim. The­ory Ap­pl. 30 : 3 (1980), pp. 383–​394. MR 567793 Zbl 0393.​90106

[2]R. J. Wil­li­ams: “Mixed strategy solu­tions for \( N \)-per­son quad­rat­ic games,” J. Op­tim. The­ory Ap­pl. 30 : 4 (1980), pp. 569–​582. MR 572156 Zbl 0396.​90114

[3]K. L. Chung and R. J. Wil­li­ams: In­tro­duc­tion to stochast­ic in­teg­ra­tion. Pro­gress in Prob­ab­il­ity and Stat­ist­ics 4. Birkhäuser (Bo­ston, MA), 1983. MR 711774 Zbl 0527.​60058 book

[4]S. R. S. Varadhan and R. J. Wil­li­ams: “Browni­an mo­tion in a wedge with ob­lique re­flec­tion,” Comm. Pure Ap­pl. Math. 38 : 4 (July 1985), pp. 405–​443. MR 792398 Zbl 0579.​60082 article

[5]R. J. Wil­li­ams: “A Feyn­man–Kac gauge for solv­ab­il­ity of the Schrödinger equa­tion,” Adv. in Ap­pl. Math. 6 : 1 (1985), pp. 1–​3. MR 776825 Zbl 0565.​35104

[6]R. J. Wil­li­ams: “Browni­an mo­tion with po­lar drift,” Trans. Amer. Math. Soc. 292 : 1 (1985), pp. 225–​246. MR 805961 Zbl 0573.​60072

[7]R. J. Wil­li­ams: “Re­cur­rence clas­si­fic­a­tion and in­vari­ant meas­ure for re­flec­ted Browni­an mo­tion in a wedge,” Ann. Probab. 13 : 3 (1985), pp. 758–​778. MR 799421 Zbl 0596.​60078

[8]R. J. Wil­li­ams: “Re­flec­ted Browni­an mo­tion in a wedge: se­mi­martin­gale prop­erty,” Z. Wahr­sch. Verw. Ge­bi­ete 69 : 2 (1985), pp. 161–​176. MR 779455 Zbl 0535.​60042

[9]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

[10]L. N. Trefeth­en and R. J. Wil­li­ams: “Con­form­al map­ping solu­tion of Laplace’s equa­tion on a poly­gon with ob­lique de­riv­at­ive bound­ary con­di­tions,” J. Com­put. Ap­pl. Math. 14 : 1–​2 (1986), pp. 227–​249. Spe­cial is­sue on nu­mer­ic­al con­form­al map­ping. MR 829041 Zbl 0596.​30014

[11]K. Burdzy and R. J. Wil­li­ams: “On Browni­an ex­cur­sions in Lipschitz do­mains. I: Loc­al path prop­er­ties,” Trans. Amer. Math. Soc. 298 : 1 (1986), pp. 289–​306. MR 857445

[12]R. J. Wil­li­ams: “Loc­al time and ex­cur­sions of re­flec­ted Browni­an mo­tion in a wedge,” Publ. Res. Inst. Math. Sci. 23 : 2 (1987), pp. 297–​319. MR 890921 Zbl 0635.​60089

[13]J. M. Har­ris­on and R. J. Wil­li­ams: “Browni­an mod­els of open queueing net­works with ho­mo­gen­eous cus­tom­er pop­u­la­tions,” Stochastics 22 : 2 (1987), pp. 77–​115. MR 912049 Zbl 0632.​60095

[14]J. M. Har­ris­on and R. J. Wil­li­ams: “Mul­ti­di­men­sion­al re­flec­ted Browni­an mo­tions hav­ing ex­po­nen­tial sta­tion­ary dis­tri­bu­tions,” Ann. Probab. 15 : 1 (1987), pp. 115–​137. MR 877593 Zbl 0615.​60072

[15]R. J. Wil­li­ams: “Re­flec­ted Browni­an mo­tion with skew sym­met­ric data in a poly­hed­ral do­main,” Probab. The­ory Re­lated Fields 75 : 4 (1987), pp. 459–​485. MR 894900 Zbl 0608.​60074

[16]R. J. Wil­li­ams: “On time-re­versal of re­flec­ted Browni­an mo­tions,” pp. 265–​276 in Sem­in­ar on stochast­ic pro­cesses, 1987 (Prin­ceton, NJ, 1987). Pro­gr. Probab. Stat­ist. 15. Birkhäuser (Bo­ston, MA), 1988. MR 1046421 Zbl 0653.​60069

[17]M. I. Re­iman and R. J. Wil­li­ams: “A bound­ary prop­erty of se­mi­martin­gale re­flect­ing Browni­an mo­tions,” Probab. The­ory Re­lated Fields 77 : 1 (1988), pp. 87–​97. MR 921820 Zbl 0617.​60081

[18]K. Burdzy, E. H. Toby, and R. J. Wil­li­ams: “On Browni­an ex­cur­sions in Lipschitz do­mains. II: Loc­al asymp­tot­ic dis­tri­bu­tions,” pp. 55–​85 in Sem­in­ar on stochast­ic pro­cesses, 1988 (Gaines­ville, FL, 1988). Pro­gr. Probab. 17. Birkhäuser (Bo­ston, MA), 1989. MR 990474

[19]K. L. Chung and R. J. Wil­li­ams: In­tro­duc­tion to stochast­ic in­teg­ra­tion, 2nd edition. Prob­ab­il­ity and its Ap­plic­a­tions. Birkhäuser (Bo­ston, MA), 1990. MR 1102676 Zbl 0725.​60050 book

[20]Sem­in­ar on stochast­ic pro­cesses, 1989 (Uni­versity of Cali­for­nia, San Diego, CA, March 30–April 1, 1989). Edi­ted by E. Çin­lar, K. L. Chung, R. K. Getoor, P. J. Fitz­sim­mons, and R. J. Wil­li­ams. Pro­gress in Prob­ab­il­ity 18. Birkhäuser (Bo­ston, MA), 1990. MR 1042337 Zbl 0686.​00017 book

[21]R. J. Wil­li­ams and W. A. Zheng: “On re­flect­ing Browni­an mo­tion — a weak con­ver­gence ap­proach,” Ann. Inst. H. Poin­caré Probab. Stat­ist. 26 : 3 (1990), pp. 461–​488. MR 1066089 Zbl 0704.​60081

[22]J. M. Har­ris­on and R. J. Wil­li­ams: “On the quasire­vers­ib­il­ity of a mul­ti­class Browni­an ser­vice sta­tion,” Ann. Probab. 18 : 3 (1990), pp. 1249–​1268. MR 1062068 Zbl 0709.​60081

[23]J. M. Har­ris­on, R. J. Wil­li­ams, and H. Chen: “Browni­an mod­els of closed queueing net­works with ho­mo­gen­eous cus­tom­er pop­u­la­tions,” Stochastics and Stochastics Re­ports 29 : 2 (1990), pp. 37–​74. Zbl 0699.​60084

[24]R. J. Wil­li­ams: “Browni­an mod­els of mul­ti­class queueing net­works,” pp. 573–​574 in Pro­ceed­ings 29th IEEE Con­fer­ence on De­cision and Con­trol, Decem­ber 1990. 1990.

[25]Sem­in­ar on stochast­ic pro­cesses, 1990 (Uni­versity of Brit­ish Columbia, Van­couver, May 10–12, 1990). Edi­ted by E. Çin­lar, P. J. Fitz­sim­mons, and R. J. Wil­li­ams. Pro­gress in Prob­ab­il­ity 24. Birkhäuser (Bo­ston, MA), 1991. MR 1118435

[26]Y. Kwon and R. J. Wil­li­ams: “Re­flec­ted Browni­an mo­tion in a cone with ra­di­ally ho­mo­gen­eous re­flec­tion field,” Trans. Amer. Math. Soc. 327 : 2 (1991), pp. 739–​780. MR 1028760 Zbl 0742.​60075

[27]J. M. Har­ris­on and R. J. Wil­li­ams: “Browni­an mod­els of feed­for­ward queueing net­works: quasire­vers­ib­il­ity and product form solu­tions,” Ann. Ap­pl. Probab. 2 : 2 (1992), pp. 263–​293. MR 1161055 Zbl 0753.​60071

[28]R. J. Wil­li­ams: “Asymp­tot­ic vari­ance para­met­ers for the bound­ary loc­al times of re­flec­ted Browni­an mo­tion on a com­pact in­ter­val,” J. Ap­pl. Probab. 29 : 4 (1992), pp. 996–​1002. MR 1188553 Zbl 0767.​60087

[29]L. M. Taylor and R. J. Wil­li­ams: “Ex­ist­ence and unique­ness of se­mi­martin­gale re­flect­ing Browni­an mo­tions in an or­thant,” Probab. The­ory Re­lated Fields 96 : 3 (1993), pp. 283–​317. MR 1231926 Zbl 0794.​60079

[30]Z. Q. Chen, P. J. Fitz­sim­mons, and R. J. Wil­li­ams: “Re­flect­ing Browni­an mo­tions: quasi­martin­gales and strong Cac­ciop­poli sets,” Po­ten­tial Anal. 2 : 3 (1993), pp. 219–​243. MR 1245240

[31]R. J. Wil­li­ams: “Re­flec­ted Browni­an mo­tion: Hunt pro­cesses and se­mi­martin­gale rep­res­ent­a­tion,” pp. 216–​221 in Bar­celona Sem­in­ar on Stochast­ic Ana­lys­is (St. Fe­liu de Guíxols, 1991). Pro­gr. Probab. 32. Birkhäuser (Basel), 1993. MR 1265051 Zbl 0844.​60051

[32]Z. Q. Chen, R. J. Wil­li­ams, and Z. Zhao: “On the ex­ist­ence of pos­it­ive solu­tions of semi­lin­ear el­lipt­ic equa­tions with Di­rich­let bound­ary con­di­tions,” Math. Ann. 298 : 3 (1994), pp. 543–​556. MR 1262775 Zbl 0790.​35038

[33]Z. Q. Chen, R. J. Wil­li­ams, and Z. Zhao: “A So­bolev in­equal­ity and Neu­mann heat ker­nel es­tim­ate for un­boun­ded do­mains,” Math. Res. Lett. 1 : 2 (1994), pp. 177–​184. MR 1266756 Zbl 0847.​46014

[34]É. Par­doux and R. J. Wil­li­ams: “Sym­met­ric re­flec­ted dif­fu­sions,” Ann. Inst. H. Poin­caré Probab. Stat­ist. 30 : 1 (1994), pp. 13–​62. MR 1262891 Zbl 0794.​60078

[35]P. Dupuis and R. J. Wil­li­ams: “Lya­pun­ov func­tions for se­mi­martin­gale re­flect­ing Browni­an mo­tions,” Ann. Probab. 22 : 2 (1994), pp. 680–​702. MR 1288127 Zbl 0808.​60068

[36]R. J. Wil­li­ams: “Se­mi­martin­gale re­flect­ing Browni­an mo­tions in the or­thant,” pp. 125–​137 in Stochast­ic net­works. IMA Vol. Math. Ap­pl. 71. Spring­er (New York), 1995. MR 1381009 Zbl 0827.​60031

[37]R. J. Wil­li­ams: “Some con­nec­tions between Browni­an mo­tion and ana­lys­is via stochast­ic cal­cu­lus,” pp. 75–​88 in Top­ics in con­tem­por­ary prob­ab­il­ity and its ap­plic­a­tions. Probab. Stochastics Ser. CRC (Boca Raton, FL), 1995. MR 1410534 Zbl 0864.​60066

[38]Z. Q. Chen, R. J. Wil­li­ams, and Z. Zhao: “Non­neg­at­ive solu­tions for semi­lin­ear el­lipt­ic equa­tions with bound­ary con­di­tions — a prob­ab­il­ist­ic ap­proach,” pp. 65–​82 in Stochast­ic ana­lys­is (Ithaca, NY, 1993). Proc. Sym­pos. Pure Math. 57. Amer. Math. Soc. (Provid­ence, RI), 1995. MR 1335463 Zbl 0833.​35044

[39]Stochast­ic net­works. Edi­ted by F. P. Kelly and R. J. Wil­li­ams. The IMA Volumes in Math­em­at­ics and its Ap­plic­a­tions 71. Spring­er (New York), 1995. MR 1381002 Zbl 0822.​90106

[40]Z. Q. Chen, R. J. Wil­li­ams, and Z. Zhao: “On the ex­ist­ence of pos­it­ive solu­tions for semi­lin­ear el­lipt­ic equa­tions with Neu­mann bound­ary con­di­tions,” Probab. The­ory Re­lated Fields 101 : 2 (1995), pp. 251–​276. MR 1318196 Zbl 0814.​35034

[41]M. Men­shikov and R. J. Wil­li­ams: “Pas­sage-time mo­ments for con­tinu­ous non-neg­at­ive stochast­ic pro­cesses and ap­plic­a­tions,” Adv. in Ap­pl. Probab. 28 : 3 (1996), pp. 747–​762. MR 1404308 Zbl 0857.​60042

[42]J. M. Har­ris­on and R. J. Wil­li­ams: “A mul­ti­class closed queueing net­work with un­con­ven­tion­al heavy traffic be­ha­vi­or,” Ann. Ap­pl. Probab. 6 : 1 (1996), pp. 1–​47. MR 1389830 Zbl 0865.​60078

[43]R. J. Wil­li­ams: “On the ap­prox­im­a­tion of queueing net­works in heavy traffic,” pp. 35–​56 in Stochast­ic net­works: The­ory and ap­plic­a­tions (Ed­in­burgh, 1–11 Au­gust 1–11 1995). Edi­ted by F. P. Kelly, S. Zachary, and I. Zied­ins. Roy­al Stat­ist­ic­al So­ci­ety Lect. Note Ser. 4. Ox­ford Uni­versity Press (Ox­ford), 1996. Zbl 0855.​60083

[44]P. J. Brock­well and R. J. Wil­li­ams: “On the ex­ist­ence and ap­plic­a­tion of con­tinu­ous-time threshold autore­gres­sions of or­der two,” Adv. in Ap­pl. Probab. 29 : 1 (1997), pp. 205–​227. MR 1432937 Zbl 0882.​60079

[45]R. J. Wil­li­ams: “Some re­cent de­vel­op­ments for queueing net­works,” pp. 340–​356 in Prob­ab­il­ity to­wards 2000 (New York, 1995). Lec­ture Notes in Stat­ist. 128. Spring­er (New York), 1998. MR 1632612 Zbl 1044.​60516

[46]R. J. Wil­li­ams: “Re­flect­ing dif­fu­sions and queueing net­works,” pp. 321–​330 in Pro­ceed­ings of the In­ter­na­tion­al Con­gress of Math­em­aticians (Ber­lin, 1998), published as Doc. Math. Extra vol.~III (1998). MR 1648166 Zbl 0933.​60102

[47]R. J. Wil­li­ams: “Dif­fu­sion ap­prox­im­a­tions for open mul­ti­class queueing net­works: suf­fi­cient con­di­tions in­volving state space col­lapse,” Queueing Sys­tems The­ory Ap­pl. 30 : 1–​2 (1998), pp. 27–​88. MR 1663759 Zbl 0911.​90171

[48]R. J. Wil­li­ams: “An in­vari­ance prin­ciple for se­mi­martin­gale re­flect­ing Browni­an mo­tions in an or­thant,” Queueing Sys­tems The­ory Ap­pl. 30 : 1–​2 (1998), pp. 5–​25. MR 1663755 Zbl 0911.​90170

[49]Z.-Q. Chen, R. J. Wil­li­ams, and Z. Zhao: “On the ex­ist­ence of pos­it­ive solu­tions for semi­lin­ear el­lipt­ic equa­tions with sin­gu­lar lower or­der coef­fi­cients and Di­rich­let bound­ary con­di­tions,” Math. Ann. 315 : 4 (1999), pp. 735–​769. MR 1731467 Zbl 0942.​35082

[50]S. N. Evans and R. J. Wil­li­ams: “Trans­ition op­er­at­ors of dif­fu­sions re­duce zero-cross­ing,” Trans. Amer. Math. Soc. 351 : 4 (1999), pp. 1377–​1389. MR 1615955 Zbl 0929.​60058

[51]S. L. Bell and R. J. Wil­li­ams: “Dy­nam­ic schedul­ing of a sys­tem with two par­al­lel serv­ers: Asymp­tot­ic op­tim­al­ity of a con­tinu­ous re­view threshold policy in heavy traffic,” pp. 2255–​2260 in Pro­ceed­ings of the 38th IEEE Con­fer­ence on De­cision and Con­trol (Phoenix, Decem­ber 1999). 1999.

[52]R. J. Wil­li­ams: “On dy­nam­ic schedul­ing of a par­al­lel serv­er sys­tem with com­plete re­source pool­ing,” pp. 49–​71 in Ana­lys­is of com­mu­nic­a­tion net­works: call centres, traffic and per­form­ance (Toronto, ON, 1998). Fields Inst. Com­mun. 28. Amer. Math. Soc. (Provid­ence, RI), 2000. MR 1788708 Zbl 0982.​90024

[53]M. Bramson and R. J. Wil­li­ams: “On dy­nam­ic schedul­ing of stochast­ic net­works in heavy traffic and some new res­ults for the work­load pro­cess,” pp. 516–​521 in Pro­ceed­ings of the 39th IEEE Con­fer­ence on De­cision and Con­trol, Decem­ber 2000. 2000.

[54]S. L. Bell and R. J. Wil­li­ams: “Dy­nam­ic schedul­ing of a sys­tem with two par­al­lel serv­ers in heavy traffic with re­source pool­ing: asymp­tot­ic op­tim­al­ity of a threshold policy,” Ann. Ap­pl. Probab. 11 : 3 (2001), pp. 608–​649. MR 1865018 Zbl 1015.​60080

[55]H. Deng, M. Kr­stić, and R. J. Wil­li­ams: “Sta­bil­iz­a­tion of stochast­ic non­lin­ear sys­tems driv­en by noise of un­known co­v­ari­ance,” IEEE Trans. Auto­mat. Con­trol 46 : 8 (2001), pp. 1237–​1253. MR 1847327 Zbl 1008.​93068

[56]H. C. Gro­moll, A. L. Puha, and R. J. Wil­li­ams: “The flu­id lim­it of a heav­ily loaded pro­cessor shar­ing queue,” Ann. Ap­pl. Probab. 12 : 3 (2002), pp. 797–​859. MR 1925442 Zbl 1017.​60092

[57]J. R. Movel­lan, P. Mineiro, and R. J. Wil­li­ams: “A Monte Carlo EM ap­proach for par­tially ob­serv­able dif­fu­sion pro­cesses: The­ory and ap­plic­a­tions to neur­al net­works,” Neur­al Com­pu­ta­tion 14 : 7 (2002), pp. 1507–​1544. Zbl 1012.​68161

[58]M. Bramson and R. J. Wil­li­ams: “Two work­load prop­er­ties for Browni­an net­works,” Queueing Syst. 45 : 3 (2003), pp. 191–​221. MR 2024178 Zbl 1131.​60305

[59]F. P. Kelly and R. J. Wil­li­ams: “Flu­id mod­el for a net­work op­er­at­ing un­der a fair band­width-shar­ing policy,” Ann. Ap­pl. Probab. 14 : 3 (2004), pp. 1055–​1083. MR 2071416 Zbl 1066.​60093

[60]A. L. Puha and R. J. Wil­li­ams: “In­vari­ant states and rates of con­ver­gence for a crit­ic­al flu­id mod­el of a pro­cessor shar­ing queue,” Ann. Ap­pl. Probab. 14 : 2 (2004), pp. 517–​554. MR 2052894 Zbl 1061.​60098

[61]W. Kang, F. P. Kelly, N. H. Lee, and R. J. Wil­li­ams: “Flu­id and Browni­an ap­prox­im­a­tions for an In­ter­net con­ges­tion con­trol mod­el,” pp. 3938–​3943 in Pro­ceed­ings of the 43rd IEEE Con­fer­ence on De­cision and Con­trol, Decem­ber 2004. 2004.

[62]S. L. Bell and R. J. Wil­li­ams: “Dy­nam­ic schedul­ing of a par­al­lel serv­er sys­tem in heavy traffic with com­plete re­source pool­ing: asymp­tot­ic op­tim­al­ity of a threshold policy,” Elec­tron. J. Probab. 10 (2005), pp. no. 33, 1044–​1115. MR 2164040 Zbl 1109.​60075

[63]J. M. Har­ris­on and R. J. Wil­li­ams: “Work­load re­duc­tion of a gen­er­al­ized Browni­an net­work,” Ann. Ap­pl. Probab. 15 : 4 (2005), pp. 2255–​2295. MR 2187295 Zbl 1096.​60036

[64]D. G. Daĭ and R. D. Vil’yams: “Let­ter to the ed­it­ors: Re­marks on our pa­per ‘Ex­ist­ence and unique­ness of se­mi­martin­gale re­flect­ing Browni­an mo­tions in con­vex poly­hedra’,” Teor. Veroy­atn. Primen. 50 : 2 (2005), pp. 409–​410. MR 2222685

[65]R. J. Wil­li­ams: In­tro­duc­tion to the math­em­at­ics of fin­ance. Gradu­ate Stud­ies in Math­em­at­ics 72. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2006. MR 2218734 Zbl 1116.​91051

[66]A. L. Puha, A. L. Sto­l­yar, and R. J. Wil­li­ams: “The flu­id lim­it of an over­loaded pro­cessor shar­ing queue,” Math. Op­er. Res. 31 : 2 (2006), pp. 316–​350. MR 2234000 Zbl 05279676

[67]J. M. Har­ris­on and R. J. Wil­li­ams: “Work­load in­ter­pret­a­tion for Browni­an mod­els of stochast­ic pro­cessing net­works,” Math. Op­er. Res. 32 : 4 (2007), pp. 808–​820. MR 2363198 Zbl 05279755

[68]W. Kang and R. J. Wil­li­ams: “An in­vari­ance prin­ciple for se­mi­martin­gale re­flect­ing Browni­an mo­tions in do­mains with piece­wise smooth bound­ar­ies,” Ann. Ap­pl. Probab. 17 : 2 (2007), pp. 741–​779. MR 2308342 Zbl 1125.​60030

[69]R. At­ar, A. Bud­hiraja, and R. J. Wil­li­ams: “HJB equa­tions for cer­tain sin­gu­larly con­trolled dif­fu­sions,” Ann. Ap­pl. Probab. 17 : 5–​6 (2007), pp. 1745–​1776. MR 2358640 Zbl 1142.​93037

[70]S. Bhard­waj, R. J. Wil­li­ams, and A. S. Acam­pora: “On the per­form­ance of a two-user MIMO down­link sys­tem in heavy traffic,” IEEE Trans. In­form. The­ory 53 : 5 (2007), pp. 1851–​1859. MR 2317145

[71]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

[72]G. Cra­ciun, J. W. Helton, and R. J. Wil­li­ams: “Ho­mo­topy meth­ods for count­ing re­ac­tion net­work equi­lib­ria,” Math. Biosci. 216 : 2 (2008), pp. 140–​149. MR 2477000 Zbl 1153.​92015

[73]H. C. Gro­moll and R. J. Wil­li­ams: “Flu­id mod­el for a data net­work with \( \alpha \)-fair band­width shar­ing and gen­er­al doc­u­ment size dis­tri­bu­tions: two ex­amples of sta­bil­ity,” pp. 253–​265 in Markov pro­cesses and re­lated top­ics: a Fest­s­chrift for Thomas G. Kur­tz. Inst. Math. Stat. Col­lect. 4. Inst. Math. Stat­ist. (Beach­wood, OH), 2008. MR 2574235 Zbl 1166.​90312

[74]S. Bhard­waj and R. J. Wil­li­ams: “Dif­fu­sion ap­prox­im­a­tion for a heav­ily loaded multi-user wire­less com­mu­nic­a­tion sys­tem with co­oper­a­tion,” Queueing Syst. 62 : 4 (2009), pp. 345–​382. MR 2546421 Zbl 1185.​60100

[75]W. N. Kang, F. P. Kelly, N. H. Lee, and R. J. Wil­li­ams: “State space col­lapse and dif­fu­sion ap­prox­im­a­tion for a net­work op­er­at­ing un­der a fair band­width shar­ing policy,” Ann. Ap­pl. Probab. 19 : 5 (2009), pp. 1719–​1780. MR 2569806 Zbl 1203.​60140

[76]H. C. Gro­moll and R. J. Wil­li­ams: “Flu­id lim­its for net­works with band­width shar­ing and gen­er­al doc­u­ment size dis­tri­bu­tions,” Ann. Ap­pl. Probab. 19 : 1 (2009), pp. 243–​280. MR 2498678 Zbl 1169.​60025

[77]M. S. Kin­nally and R. J. Wil­li­ams: “On ex­ist­ence and unique­ness of sta­tion­ary dis­tri­bu­tions for stochast­ic delay dif­fer­en­tial equa­tions with pos­it­iv­ity con­straints,” Elec­tron. J. Probab. 15 (2010), pp. no. 15, 409–​451. MR 2639731

[78]F. P. Kelly and R. J. Wil­li­ams: “Heavy traffic on a con­trolled mo­tor­way,” pp. 416–​445 in Prob­ab­il­ity and math­em­at­ic­al ge­net­ics. Lon­don Math. Soc. Lec­ture Note Ser. 378. Cam­bridge Univ. Press, 2010. MR 2744250 Zbl 1208.​90036

[79]N. A. Cook­son, W. H. Math­er, T. Danino, O. Mon­drag­on-Pa­lo­mino, R. J. Wil­li­ams, L. S. Tsim­ring, and J. Hasty: “Queueing up for en­zymat­ic pro­cessing: Cor­rel­ated sig­nal­ing through coupled de­grad­a­tion,” Mo­lecu­lar Sys­tems Bio­logy 7 (2011).

[80]W. H. Math­er, J. Hasty, L. S. Tsim­ring, and R. J. Wil­li­ams: “Fac­tor­ized time-de­pend­ent dis­tri­bu­tions for cer­tain mul­ti­class queueing net­works and an ap­plic­a­tion to en­zymat­ic pro­cessing net­works,” Queueing Syst. 69 : 3–​4 (2011), pp. 313–​328. MR 2886472 Zbl 1238.​60104

[81]W. N. Kang and R. J. Wil­li­ams: “Dif­fu­sion ap­prox­im­a­tion for an in­put-queued switch op­er­at­ing un­der a max­im­um weight match­ing policy,” Stochast­ic Sys­tems 2 (2012), pp. 277–​321.