Conditioned Point Processes with Application to Levy Bridges
| Autor: | Sylvie Rœlly, Giovanni Conforti, Tetiana Kosenkova |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
General Mathematics Mathematical analysis Institut für Mathematik Poisson distribution Constructive Lévy process Point process symbols.namesake Mathematics::Probability Simple (abstract algebra) Functional equation Poisson point process symbols Jump Statistics Probability and Uncertainty ddc:510 Mathematics - Probability Mathematics |
| Popis: | Our first result concerns a characterization by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalized version of Mecke’s formula. En passant, it also allows us to gain quantitative results about stochastic domination for Poisson point processes under linear constraints. Since bridges of a pure jump Levy process in $$\mathbb {R}^d$$ with a height $$\mathfrak {a}$$ can be interpreted as a Poisson point process on space–time conditioned by pinning its first moment to $$\mathfrak {a}$$ , our approach allows us to characterize bridges of Levy processes by means of a functional equation. The latter result has two direct applications: First, we obtain a constructive and simple way to sample Levy bridge dynamics; second, it allows us to estimate the number of jumps for such bridges. We finally show that our method remains valid for linearly perturbed Levy processes like periodic Ornstein–Uhlenbeck processes driven by Levy noise. |
| Databáze: | OpenAIRE |
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