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.
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页码：223 / 235
页数：13
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