Finiteness of hitting times under taboo

Abstract

We consider a continuous-time Markov chain with a finite or countable state space. For a site y and subset H of the state space, the hitting time of y under taboo H is defined to be infinite if the process trajectory hits H before y, and the first hitting time of y otherwise. We investigate the probability that such times are finite. In particular, if the taboo set is finite, an efficient iterative scheme reduces the study to the known case of a singleton taboo. A similar procedure applies in the case of finite complement of the taboo set. The study is motivated by classification of branching processes with finitely many catalysts. Keywords and phrases: Markov chain, hitting time, taboo probabilities, catalytic branching process.

Cited by in corpus (6)

• Spread of a Catalytic Branching Random Walk on a Multidimensional Lattice
• Maximum of Catalytic Branching Random Walk with Regularly Varying Tails
• Classification of catalytic branching processes and structure of the criticality set
• Strong and weak convergence of population size in supercritical catalytic branching process
• Fluctuations of propagation front in catalytic branching walk
• Catalytic Branching Random Walk with Semi-exponential Increments