Search results for "Random walk jumps"

On the analysis of a random walk-jump chain with tree-based transitions and its applications to faulty dichotomous search

2018

Random Walks (RWs) have been extensively studied for more than a century [1]. These walks have traditionally been on a line, and the generalizations for two and three dimensions, have been by extending the random steps to the corresponding neighboring positions in one or many of the dimensions. Among the most popular RWs on a line are the various models for birth and death processes, renewal processes and the gambler’s ruin problem. All of these RWs operate “on a discretized line”, and the walk is achieved by performing small steps to the current-state’s neighbor states. Indeed, it is this neighbor-step motion that renders their analyses tractable. When some of the transitions are to non-ne…