Stochastic differential equations for sticky Brownian motion

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2014-10-24 DOI:10.1080/17442508.2014.899600

H. Engelbert, G. Peskir

引用次数: 78

Abstract

We study (i) the stochastic differential equation (SDE) systemfor Brownian motion X in sticky at 0, and (ii) the SDE systemfor reflecting Brownian motion X in sticky at 0, where X starts at x in the state space, is a given constant, is a local time of X at 0 and B is a standard Brownian motion. We prove that both systems (i) have a jointly unique weak solution and (ii) have no strong solution. The latter fact verifies Skorokhod's conjecture on sticky Brownian motion and provides alternative arguments to those given in the literature.

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粘性布朗运动的随机微分方程

我们研究了(i)粘性0处布朗运动X的随机微分方程(SDE)系统，以及(ii)反映粘性0处布朗运动X的随机微分方程系统，其中X在状态空间中从X开始，是给定常数，是X在0处的局部时间，B是标准布朗运动。证明了两个系统(i)有一个联合唯一的弱解，(ii)没有强解。后一个事实证实了斯科罗霍德关于粘性布朗运动的猜想，并提供了文献中给出的替代论据。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.