On collisions of brownian particles

Annals of Applied Probability

Volumn 20, Issue 3, 2010, Pages 951-977

  Ichiba, Tomoyuki ^a   Karatzas, Ioannis ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Intech Investment Management   (United States)

Author keywords

Atlas model; Bessel process; Comparison theorem; Effective dimension; Martingale problem; Reflected Brownian motion; Triple collision

Indexed keywords

EID: 77953839938     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/09-AAP641     Document Type: Article

References (26)

1. Banner, A. D., Fernholz, R. and Karatzas, I. (2005). Atlas models of equity markets. Ann. Appl. Probab. 15 2296-2330. MR2187296
2. Banner, A. D. and Ghomrasni, R. (2008). Local times of ranked continuous semimartin-gales. Stochastic Process. Appl. 118 1244-1253. MR2428716
3. Bass, R. F. and Pardoux, É. (1987). Uniqueness for diffusions with piecewise constant coefficients. Probab. Theory Related Fields 76 557-572. MR917679
4. Burdzy, K. and Marshall, D. (1992). Hitting a boundary point with reflected Brownian motion. In Séminaire de Probabilités, XXVI. Lecture Notes in Mathematics 1526 81-94. Springer, Berlin. MR1231985
5. Cépa, E. and Lépingle, D. (2007). No multiple collisions for mutually repelling Brownian particles. In Séminaire de Probabilités XL. Lecture Notes in Mathematics 1899 241-246. Springer, Berlin. MR2409009
6. Delarue, F. (2008). Hitting time of a corner for a reflected diffusion in the square. Ann. Inst. Henri Poincaré Probab. Stat. 44 946-961. MR2453777
7. Elworthy, K. D., Li, X.-M. and Yor, M. (1999). The importance of strictly local martingales; applications to radial Ornstein-Uhlenbeck processes. Probab. Theory Related Fields 115 325-355. MR1725406
8. Fernholz, E. R. (2002). Stochastic Portfolio Theory. Stochastic Modelling and Applied Probability 48. Springer, New York. MR1894767
9. Friedman, A. (1974). Nonattainability of a set by a diffusion process. Trans. Amer. Math. Soc. 197 245-271. MR0346903
10. Göing-Jaeschke, A. and Yor, M. (2003). A survey and some generalizations of Bessel processes. Bernoulli 9 313-349. MR1997032
11. Harrison, J. M. and Reiman, M. I. (1981). Reflected Brownian motion on an orthant. Ann. Probab. 9 302-308. MR606992
12. Harrison, J. M. and Williams, R. J. (1987). Brownian models of open queueing networks with homogeneous customer populations. Stochastics 22 77-115. MR912049
13. Ichiba, T. (2006). Note on Atlas model of equity markets. Mimeo.
14. Ikeda, N. and Watanabe, S. (1977). A comparison theorem for solutions of stochastic differential equations and its applications. Osaka J. Math. 14 619-633. MR0471082
15. Karatzas, I. and Shreve, S. E. (1991). Brownian Motion and Stochastic Calculus, 2nd ed. Graduate Texts in Mathematics 113. Springer, New York. MR1121940
16. Krylov, N. V. (1980). Controlled Diffusion Processes. Applications of Mathematics 14. Springer, New York. MR601776
17. Krylov, N. V. (2004). On weak uniqueness for some diffusions with discontinuous coefficients. Stochastic Process. Appl. 113 37-64. MR2078536
18. Meyers, N. and Serrin, J. (1960). The exterior Dirichlet problem for second order elliptic partial differential equations. J. Math. Mech. 9 513-538. MR0117421
19. Pal, S. and Pitman, J. (2008). One-dimensional Brownian particle systems with rank-dependent drifts. Ann. Appl. Probab. 18 2179-2207. MR2473654
20. Ramasubramanian, S. (1983). Recurrence of projections of diffusions. Sankhya- Ser. A 45 20-31. MR749350
21. Ramasubramanian, S. (1988). Hitting of submanifolds by diffusions. Probab. Theory Related Fields 78 149-163. MR940875
22. Rogers, L. C. G. (1990). Brownian motion in a wedge with variable skew reflection. II. In Diffusion Processes and Related Problems in Analysis I. Progress in Probability 22 95-115. Birkḧuser, Boston, MA. MR1110159
23. Rogers, L. C. G. (1991). Brownian motion in a wedge with variable skew reflection. Trans Amer. Math. Soc. 326 227-236. MR1008701
24. Stroock, D. W. and Varadhan, S. R. S. (2006). Multidimensional Diffusion Processes. Springer, Berlin. MR2190038
25. Varadhan, S. R. S. and Williams, R. J. (1985). Brownian motion in a wedge with oblique reflection. Comm. Pure Appl. Math. 38 405-443. MR792398
26. Williams, R. J. (1987). Reflected Brownian motion with skew symmetric data in a polyhedral domain. Probab. Theory Related Fields 75 459-485. MR894900