期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2019
卷号：XVI
期号：1
页码：33-47
DOI：10.30757/ALEA.v16-03
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：Our model consists of a Brownian particle X moving in R, where aPoissonian eld of moving traps is present. Each trap is a ball with constantradius, centered at a trap point, and each trap point moves under a Brownianmotion independently of others and of the motion of X. Here, we investigate the`speed' of X on the time interval [0; t] and on `microscopic' time scales given thatX avoids the trap eld up to time t. Firstly, following the earlier work of Athreyaet al. (2017), we obtain bounds on the maximal displacement of X from the origin.Our upper bound is an improvement of the corresponding bound therein. Then, weprove a result showing how the speed on microscopic time scales a ect the overallmacroscopic subdi usivity on [0; t]. Finally, we show that X moves subdi usivelyeven on certain microscopic time scales, in the bulk of [0; t]. The results are statedso that each gives an `optimal survival strategy' for the system. We conclude bygiving several related open problems.
关键词：Brownian motion in random environment; Poissonian traps; moving;trap eld; subdi usive; optimal survival strategy
