A limit theorem for singular stochastic differential equations

被引：0

作者：

Pilipenko, Andrey ^{[1
,2
]}

Prykhodko, Yuriy ^{[2
]}

机构：

[1] NAS Ukraine, Inst Math, Dept Stochast Proc, UA-01601 Kiev, Ukraine

[2] Natl Tech Univ Ukraine KPI, Dept Math Anal & Probabil Theory, Peremohy Ave 37, UA-03056 Kiev, Ukraine

来源：

MODERN STOCHASTICS-THEORY AND APPLICATIONS | 2016年 / 3卷 / 03期

关键词：

Bessel process; skew Bessel process; limit theorems;

D O I：

10.15559/16-VMSTA63

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 study the weak limits of solutions to SDEs dX(n)(t) = a(n)(X-n(t)) dt + dW(t), where the sequence {a(n)} converges in some sense to (c-1 (x< 0)+ c + 1 (x> 0))/x + gamma delta(0) Here delta(0) is the Dirac delta function concentrated at zero. A limit of {X-n} may be a Bessel process, a skew Bessel process, or a mixture of Bessel processes.

引用

页码：223 / 235

页数：13

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