The extremal process of super-Brownian motion

Stochastic Processes and their Applications - Tập 137 - Trang 1-34 - 2021
Yan-Xia Ren1, Renming Song2, Rui Zhang3
1LMAM School of Mathematical Sciences & Center for Statistical Science, Peking University, Beijing 100871, PR China
2Department of Mathematics, University of Illinois, Urbana, IL 61801, USA
3School of Mathematical Sciences & Academy for Multidisciplinary Studies, Capital Normal University, Beijing, 100048, PR China

Tài liệu tham khảo

Aïdékon, 2013, Convergence in law of the minimum of a branching random walk, Ann. Probab., 41, 1362, 10.1214/12-AOP750 Aïdékon, 2013, Branching Brownian motion seen from its tip, Probab. Theory Related Fields, 157, 405, 10.1007/s00440-012-0461-0 Arguin, 2011, Genealogy of extremal particles of branching Brownian motion, Comm. Pure Appl. Math., 64, 1647, 10.1002/cpa.20387 Arguin, 2012, Poissonian statistics in the extremal process of branching Brownian motion, Ann. Appl. Probab., 22, 1693, 10.1214/11-AAP809 Arguin, 2013, The extremal process of branching Brownian motion, Probab. Theory Related Fields, 157, 535, 10.1007/s00440-012-0464-x Aronson, 1978, Multidimensional nonlinear diffusion arising in population genetics, Adv. Math., 30, 33, 10.1016/0001-8708(78)90130-5 J. Berestycki, E. Brunet, A. Cortines, B. Mallein, Extremes of branching Ornstein–Uhlenbeck processes. Preprint. arXiv:1810.05809v1. Bocharov, 2020, Limiting distribution of particles near the frontier in the catalytic branching Brownian motion, Acta Appl. Math., 169, 433, 10.1007/s10440-019-00305-w Bocharov, 2014, Branching Brownian motion with catalytic branching at the origin, Acta Appl. Math., 134, 201, 10.1007/s10440-014-9879-y Bocharov, 2016, Limiting distribution of the rightmost particle in catalytic branching Brownian motion, Electron. Commun. Probab., 21, 70, 10.1214/16-ECP22 Bovier, 2017 Bramson, 1978, Maximal displacement of branching Brownian motion, Comm. Pure Appl. Math., 31, 531, 10.1002/cpa.3160310502 Bramson, 1983, Convergence of solutions of the Kolmogorov equation to travelling waves, Mem. Amer. Math. Soc., 44, iv+190 Carmona, 2014, The spread of a catalytic branching random walk, Ann. Inst. Henri Poincaré Probab. Stat., 50, 327, 10.1214/12-AIHP529 Chauvin, 1988, KPP equation and supercritical branching Brownian motion in the subcritical speed area. Application to spatial trees, Probab. Theory Related Fields, 80, 299, 10.1007/BF00356108 Chauvin, 1990, Supercritical branching Brownian motion and K-P-P equation in the critical speed-area, Math. Nachr., 149, 41, 10.1002/mana.19901490104 Dawson, 1991, Measure-valued Markov Processes, vol. 1541, 1 Dynkin, 1993, Superprocesses and partial differential equations, Ann. Probab., 21, 1185, 10.1214/aop/1176989116 Englander, 2004, Large deviations for the growth rate of the support of supercritical super-Brownian motion, Statist. Probab. Lett., 66, 449, 10.1016/j.spl.2003.12.003 Fisher, 1937, The advance of advantageous genes, Ann. Eugen., 7, 355, 10.1111/j.1469-1809.1937.tb02153.x Harris, 1999, Travelling-waves for the FKPP equation via probabilistic arguments, Proc. Roy. Soc. Edinburgh Sect. A, 129, 503, 10.1017/S030821050002148X Hu, 2009, Minimal position and critical martingale convergence in branching random walks, and directed polymers on disordered trees, Ann. Probab., 37, 742, 10.1214/08-AOP419 Ikeda, 1968, Markov branching processes, I, J. Math. Kyoto Univ., 8, 233 Ikeda, 1968, Markov branching processes, II, J. Math. Kyoto Univ., 8, 365 Ikeda, 1968, Markov branching processes, III, J. Math. Kyoto Univ., 9, 95 Kallenberg, 1997 Kallenberg, 2017 Kolmogorov, 1937, Étude de l’équation de la diffusion avec croissance de la quantité de la matière at son application à un problem biologique, Moscow Univ. Math. Bull., 1, 1 Kyprianou, 2004, Travelling wave solutions to the K-p-P equation: alternatives to Simon Harris’ probabilistic analysis, Ann. Inst. Henri Poincaré Probab. Stat., 40, 53, 10.1016/S0246-0203(03)00055-4 Kyprianou, 2012, Supercritical super-Brownian motion with a general branching mechanism and travelling waves, Ann. Inst. Henri Poincaré Probab. Stat., 48, 661, 10.1214/11-AIHP448 Lalley, 1987, A conditional limit theorem for the frontier of branching Brownian motion, Ann. Probab., 15, 1052, 10.1214/aop/1176992080 Lalley, 1988, Travelling waves in inhomogeneous branching Brownian motions I, Ann. Probab., 16, 1051, 10.1214/aop/1176991677 Lalley, 1989, Travelling waves in inhomogeneous branching Brownian motions II, Ann. Probab., 17, 116, 10.1214/aop/1176991498 Lau, 1985, On the nonlinear diffusion equation of Kolmogorov, Petrovsky, and Piscounov, J. Differential Equations, 59, 44, 10.1016/0022-0396(85)90137-8 Li, 2011 Madaule, 2017, Convergence in law for the branching random walk seen from its tip, J. Theoret. Probab., 30, 27, 10.1007/s10959-015-0636-6 Maillard, 2013, A note on stable point processes occurring in branching Brownian motion, Electron. Commun. Probab., 18, 5, 10.1214/ECP.v18-2390 McKean, 1975, Application of Brownian motion to the equation of Kolmogorov- Petrovskii-Piskunov, Comm. Pure Appl. Math., 28, 323, 10.1002/cpa.3160280302 Nishimori, 2019 Pinsky, 1995, K-p-p-type asymptotics for nonlinear diffusion in a large ball with infinite boundary data and on Rd with infinite initial data outside a large ball, Comm. Partial Differential Equations, 20, 1369, 10.1080/03605309508821136 Protter, 1967 Roberts, 2013, A simple path to asymptotics for the frontier of a branching Brownian motion, Ann. Probab., 41, 3518, 10.1214/12-AOP753 Sheu, 1997, Lifetime and compactness of range for super-Brownian motion with a general branching mechanism, Stochastic Process. Appl., 70, 129, 10.1016/S0304-4149(97)00059-8 Shiozawa, 2018, Spread rate of branching Brownian motions, Acta Appl. Math., 155, 113, 10.1007/s10440-017-0148-8 Volpert, 1994, vol. 140