Stochastic integral equations for Walsh semimartingales

被引：9

作者：

Ichiba, Tomoyuki ^{[1
]}

Karatzas, Ioannis ^{[2
,4
]}

Prokaj, Vilmos ^{[1
,3
]}

Yan, Minghan ^{[2
]}

机构：

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

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

[3] Eotvos Lorand Univ, Dept Probabil Theory & Stat, Pazmany Peter Setany 1-C, H-1117 Budapest, Hungary

[4] INTECH Investment Management, One Palmer Sq,Suite 441, Princeton, NJ 08542 USA

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2018年 / 54卷 / 02期

基金：

美国国家科学基金会;

关键词：

Skew and Walsh Brownian motions; Spider and Walsh semimartingales; Skorokhod reflection; Planar skew unfolding; Harrison-Shepp equations; Freidlin-Sheu formula; Martingale problems; Local time; BROWNIAN-MOTION; DIFFERENTIAL-EQUATIONS; DIFFUSION-PROCESSES; REFLECTION;

D O I：

10.1214/16-AIHP819

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 planar semimartingales that include the Walsh Brownian motion as a special case, and derive Harrison-Shepp-type equations and a change-of-variable formula in the spirit of Freidlin-Sheu for these so-called "Walsh semimartingales". We examine the solvability of the resulting system of stochastic integral equations. In appropriate Markovian settings we study two types of connections to martingale problems, questions of uniqueness in distribution for such processes, and a few examples.

引用

页码：726 / 756

页数：31

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