Diffusions with rank-based characteristics and values in the nonnegative quadrant

被引：4

作者：

Ichiba, Tomoyuki ^{[1
]}

Karatzas, Ioannis ^{[2
,3
]}

Prokaj, Vilmos ^{[4
]}

机构：

[1] Univ Calif Santa Barbara, Dept Stat & Appl Probabil, Santa Barbara, CA 93106 USA

[2] INTECH Investment Management LLC, Princeton, NJ 08542 USA

[3] Columbia Univ, Dept Math, New York, NY 10027 USA

[4] Eotvos Lorand Univ, Dept Probabil Theory & Stat, H-1117 Budapest, Hungary

来源：

BERNOULLI | 2013年 / 19卷 / 5B期

基金：

美国国家科学基金会;

关键词：

diffusion with reflection and rank-dependent characteristics; semimartingale local time; skew representations; Skorokhod problem; sum-of-exponential stationary densities; Tanaka formula and equation; unfolding nonnegative semimartingales; weak and strong solutions; REFLECTING BROWNIAN MOTIONS; ATLAS MODELS; SEMIMARTINGALE; COEFFICIENTS; UNIQUENESS; WEDGE;

D O I：

10.3150/12-BEJ459

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 construct diffusions with values in the nonnegative orthant, normal reflection along each of the axes, and two pairs of local drift/variance characteristics assigned according to rank; one of the variances is allowed to vanish, but not both. The construction involves solving a system of coupled Skorokhod reflection equations, then "unfolding" the Skorokhod reflection of a suitable semimartingale in the manner of Prokaj (Statist. Probab. Lett. 79 (2009) 534-536). Questions of pathwise uniqueness and strength are also addressed, for systems of stochastic differential equations with reflection that realize these diffusions. When the variance of the laggard is at least as large as that of the leader, it is shown that the corner of the quadrant is never visited.

引用

页码：2455 / 2493

页数：39

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