Applied Mathematics Commons^™

Random Walks On Random Lattices And Their Applications, Ryan Tyler White

Theses and Dissertations

This work studies a class of continuous-time, multidimensional random walk processes with mutually dependent random step sizes and their exits from hyperrectangles. Fluctuations of the process about the critical boundary are studied extensively by stochastic analysis and operational calculus. Further, information on the process can be ascertained only upon observations occurring according to a delayed renewal process, rather than in real time. Passage times are thus obscured and results are first derived pertaining to the pre-passage and post-passage observations. Two distinct strategies are developed to combat the crudeness of delayed observations in order to derive more refined information about the …