An overshoot approach to recurrence and transience of Markov processes
| Autor: | Björn Böttcher |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Statistics and Probability
Pure mathematics Markov chain Generator (category theory) Stable-like processes Applied Mathematics Markov process Time reversibility symbols.namesake Recurrence Modeling and Simulation Modelling and Simulation Transience Calculus Overshoot (signal) symbols Markov processes with jumps Mathematics - Probability Mathematics |
| Zdroj: | Stochastic Processes and their Applications. 121(9):1962-1981 |
| ISSN: | 0304-4149 |
| DOI: | 10.1016/j.spa.2011.05.010 |
| Popis: | We develop criteria for recurrence and transience of one-dimensional Markov processes which have jumps and oscillate between + ∞ and − ∞ . 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 − ( − Δ ) α ( x ) / 2 such that α ( x ) = α for x − R and α ( x ) = β for x > R for some R > 0 and α , β ∈ ( 0 , 2 ) is transient if and only if α + β 2 , otherwise it is recurrent. As a special case, this yields a new proof for the recurrence, point recurrence and transience of symmetric α -stable processes. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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