FROM BROWNIAN MOTION WITH A LOCAL TIME DRIFT TO FELLER'S BRANCHING DIFFUSION WITH LOGISTIC GROWTH

被引：9

作者：

Pardoux, Etienne ^{[1
]}

Wakolbinger, Anton ^{[2
]}

机构：

[1] Univ Aix Marseille 1, F-13331 Marseille 3, France

[2] Goethe Univ Frankfurt, D-6000 Frankfurt, Germany

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2011年 / 16卷

关键词：

Ray-Knight representation; local time; Feller branching with logistic growth; Brownian motion; local time drift; Girsanov transform;

D O I：

10.1214/ECP.v16-1679

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We give a new proof for a Ray-Knight representation of Feller's branching diffusion with logistic growth in terms of the local times of a reflected Brownian motion H with a drift that is affine linear in the local time accumulated by H at its current level. In [5], such a representation was obtained by an approximation through Harris paths that code the genealogies of particle systems. The present proof is purely in terms of stochastic analysis, and is inspired by previous work of Norris, Rogers and Williams [7].

引用

页码：720 / 731

页数：12

共 50 条

[31] α-TIME FRACTIONAL BROWNIAN MOTION: PDE CONNECTIONS AND LOCAL TIMES
Nane, Erkan
Wu, Dongsheng
Xiao, Yimin
ESAIM-PROBABILITY AND STATISTICS, 2012, 16 : 1 - 24
[32] Local time and Tanaka formula for the G-Brownian motion
Lin, Qian
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 398 (01) : 315 - 334
[33] On the boundary local time measure of super-Brownian motion
Hong, Jieliang
ELECTRONIC JOURNAL OF PROBABILITY, 2020, 25 : 1 - 66
[34] Large deviations for local time fractional Brownian motion and applications
Meerschaert, Mark M.
Nane, Erkan
Xiao, Yimin
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 346 (02) : 432 - 445
[35] Almost sure asymptotics for the local time of a diffusion in Brownian environment
Diel, Roland
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2011, 121 (10) : 2303 - 2330
[36] Rough path analysis for local time of G-Brownian motion
Yan, Litan
Li, Yumiao
He, Kun
APPLICABLE ANALYSIS, 2020, 99 (06) : 899 - 921
[37] Generalized grey Brownian motion local time: existence and weak approximation
da Silva, Jose Luis
Erraoui, Mohamed
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2015, 87 (02) : 347 - 361
[38] Martingale approximation for self-intersection local time of Brownian motion
de Faria, M
Rezgui, A
Streit, L
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON STOCHASTIC ANALYSIS AND APPLICATIONS, 2004, : 95 - 106
[39] CHAOS EXPANSIONS OF DOUBLE INTERSECTION LOCAL TIME OF BROWNIAN-MOTION IN R(D) AND RENORMALIZATION
IMKELLER, P
PEREZABREU, V
VIVES, J
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1995, 56 (01) : 1 - 34
[40] Integration with Respect to Self-Intersection Local Time of a One-Dimensional Brownian Motion
Najnudel, Joseph
SEMINAIRE DE PROBABILITES XL, 2007, 1899 : 105 - 116

← 1 2 3 4 5 →