A class of discrete time stochastic processes defined on infinite trees is in- troduced. Moving from a vertex ν, each process in this class has an initial preferred direction; this latter definitively disappears when a finite set of vertices associated to ν is completely explored. We prove the transience of some processes in this class. As a strictly related result, we also solve a conjecture formulated by Volkov (2003) on the long- term behavior of his digging random walk.
On a new class of non-markovian processes defined on trees / Agnese Panzera. - (2007).
On a new class of non-markovian processes defined on trees
PANZERA, AGNESE
2007
Abstract
A class of discrete time stochastic processes defined on infinite trees is in- troduced. Moving from a vertex ν, each process in this class has an initial preferred direction; this latter definitively disappears when a finite set of vertices associated to ν is completely explored. We prove the transience of some processes in this class. As a strictly related result, we also solve a conjecture formulated by Volkov (2003) on the long- term behavior of his digging random walk.
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