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An overshoot approach to recurrence and transience of Markov processes


  • Böttcher, Björn


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]

Suggested Citation

  • Böttcher, Björn, 2011. "An overshoot approach to recurrence and transience of Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 1962-1981, September.
  • Handle: RePEc:eee:spapps:v:121:y:2011:i:9:p:1962-1981

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