We provide sufficient conditions for the persistence or transience of stochastic processes on the real line based on the behavior of the first and second moments of their conditional increments at the boundaries. Our findings extend previous results in the literature (Lamperti, 1960) to the large class of discrete-time processes with bounded increments. We present some examples of application by studying the survival and dominance of agents trading incomplete financial markets.

Drift criteria for persistence of discrete stochastic processes on the line

Giulio Bottazzi
;
Pietro DIndo
2022

Abstract

We provide sufficient conditions for the persistence or transience of stochastic processes on the real line based on the behavior of the first and second moments of their conditional increments at the boundaries. Our findings extend previous results in the literature (Lamperti, 1960) to the large class of discrete-time processes with bounded increments. We present some examples of application by studying the survival and dominance of agents trading incomplete financial markets.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11382/546131
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