A New Markov Selection Procedure for Degenerate Diffusions

被引：9

作者：

Borkar, V. S. ^{[1
]}

Kumar, K. Suresh ^{[2
]}

机构：

[1] Tata Inst Fundamental Res, Sch Technol & Comp Sci, Mumbai 400005, Maharashtra, India

[2] Indian Inst Technol, Dept Math, Mumbai 400076, Maharashtra, India

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2010年 / 23卷 / 03期

关键词：

Degenerate diffusions; Markov selection; Feller process; Small noise limit; Backward Kolmogorov equation; Viscosity solutions; VISCOSITY SOLUTIONS; EQUATIONS; COEFFICIENTS; ATTRACTORS; UNIQUENESS; EXISTENCE;

D O I：

10.1007/s10959-009-0242-6

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：

A new selection principle is proposed for construction of a Feller solution to an ill-posed degenerate diffusion process. This is based on constructing the Feller transition kernel from the unique (under suitable conditions) continuous viscosity solutions to the backward Kolmogorov equation associated with the diffusion. The connection of this Feller process with the small-noise limits of the nondegenerate perturbations of the diffusion and several other related phenomena are also discussed.

引用

页码：729 / 747

页数：19

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