An overshoot approach to recurrence and transience of Markov processes

Björn Böttcher

Stochastic Processes and their Applications, 2011, vol. 121, issue 9, 1962-1981

Abstract: We develop criteria for recurrence and transience of one-dimensional Markov processes which have jumps and oscillate between +[infinity] and -[infinity]. The conditions are based on a Markov chain which only consists of jumps (overshoots) of the process into complementary parts of the state space. In particular, we show that a stable-like process with generator -(-[Delta])[alpha](x)/2 such that [alpha](x)=[alpha] for x R for some R>0 and [alpha],[beta][set membership, variant](0,2) is transient if and only if [alpha]+[beta]

Keywords: Markov; processes; with; jumps; Recurrence; Transience; Stable-like; processes (search for similar items in EconPapers)
Date: 2011
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