广义高斯势下布朗运动的淬灭渐近性

IF 2.1 1区数学 Q1 STATISTICS & PROBABILITY

Annals of Probability Pub Date : 2014-02-25 DOI:10.1214/12-AOP830

Xia Chen

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引用次数: 41

摘要

本文研究了由$d$维布朗运动$\{B_s;s\ge 0\}$和广义高斯场$V$组成的淬火力矩\[\mathbb{E}_x\exp \biggl\{\int_0^tV(B_s)\,ds\biggr\}\]的长期渐近性。本文取得的主要进展包括:对Carmona和Molchanov发表的一个开放问题的解法[Probab]。理论相关领域102(1995)433-453]，在牛顿型势和由白噪声或分数白噪声驱动的势中布朗运动的淬灭定律。

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Quenched asymptotics for Brownian motion in generalized Gaussian potential

In this paper, we study the long-term asymptotics for the quenched moment \[\mathbb{E}_x\exp \biggl\{\int_0^tV(B_s)\,ds\biggr\}\] consisting of a $d$-dimensional Brownian motion $\{B_s;s\ge 0\}$ and a generalized Gaussian field $V$. The major progress made in this paper includes: Solution to an open problem posted by Carmona and Molchanov [Probab. Theory Related Fields 102 (1995) 433-453], the quenched laws for Brownian motions in Newtonian-type potentials and in the potentials driven by white noise or by fractional white noise.

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来源期刊

Annals of Probability 数学-统计学与概率论

CiteScore

4.60

自引率

8.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Annals of Probability publishes research papers in modern probability theory, its relations to other areas of mathematics, and its applications in the physical and biological sciences. Emphasis is on importance, interest, and originality – formal novelty and correctness are not sufficient for publication. The Annals will also publish authoritative review papers and surveys of areas in vigorous development.