Öz, Mehmet2020-08-282020-08-2820191980-0436http://hdl.handle.net/10679/6852https://doi.org/10.30757/ALEA.v16-03Our model consists of a Brownian particle X moving in N, where a Poissonian field of moving traps is present. Each trap is a ball with constant radius, centered at a trap point, and each trap point moves under a Brownian motion 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 that X avoids the trap field up to time t. Firstly, following the earlier work of 'Athreya. et 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, we prove a result showing how the speed on microscopic time scales affect the overall macroscopic subdiffusivity on [0, t]. Finally, we show that X moves subdiffusively even on certain microscopic time scales, in the bulk of [0, t]. The results are stated so that each gives an 'optimal survival strategy' for the system. We conclude by giving several related open problems.engopenAccessarticle161334700047658830000310.30757/ALEA.v16-03Brownian motion in random environmentPoissonian trapsMoving trap fieldSubdiffusiveOptimal survival strategy2-s2.0-85070019836