Levy processes with finite variance conditioned to avoid an interval
| Autor: | Philip Weissmann, Alexander R. Watson, Leif Döring |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
media_common.quotation_subject Markov process Interval (mathematics) 01 natural sciences Lévy process 010104 statistics & probability symbols.namesake martingales 60J25 Killed process Overshoot (signal) FOS: Mathematics Applied mathematics 60G44 0101 mathematics media_common Mathematics Markov processes 010102 general mathematics Probability (math.PR) Doob $h$-transform Process (computing) Infinity Lévy processes Path (graph theory) symbols killed Lévy processes Statistics Probability and Uncertainty 60G51 Mathematics - Probability |
| Zdroj: | Doring, L, Watson, A R & Weissmann, P 2019, ' Levy processes with finite variance conditioned to avoid an interval ', Electronic Journal of Probability . < https://projecteuclid.org/euclid.ejp/1559700305#info > MADOC-University of Mannheim Electron. J. Probab. |
| Popis: | Conditioning Markov processes to avoid a set is a classical problem that has been studied in many settings. In the present article we study the question if a Levy process can be conditioned to avoid an interval and, if so, the path behavior of the conditioned process. For Levy processes with finite second moments we show that conditioning is possible and identify the conditioned process as an h-transform of the original killed process. The h-transform is explicit in terms of successive overshoot distributions and is used to prove that the conditioned process diverges to plus infinity and minus infinity with positive probabilities. Comments welcome! |
| Databáze: | OpenAIRE |
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