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 moment of their conditional increments at the boundaries. Our findings ex- tend 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 survival and dominance of agents trading in complete financial markets.
Drift criteria for persistence of discrete stochastic processes on the line
Dindo Pietro
2022-01-01
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 moment of their conditional increments at the boundaries. Our findings ex- tend 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 survival and dominance of agents trading in complete financial markets.
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