Self-similarity and Lamperti convergence for families of stochastic processes
| Autor: | Clarice Garcia Borges Demétrio, Bent Jørgensen, José Raúl Martínez |
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| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: |
Stochastic process
60G18 (Primary) 60G22 60F05 (Secondary) General Mathematics Mathematical analysis Mathematics - Statistics Theory Statistics Theory (math.ST) Covariance Lévy process Inverse Gaussian distribution symbols.namesake Mathematics::Probability Moving average Ordinary differential equation FOS: Mathematics symbols Limit (mathematics) Statistical physics Brownian motion Mathematics |
| Zdroj: | Jørgensen, B, Martínez, J R & Demétrio, C G B 2011, ' Self-similarity and Lamperti convergence for families of stochastic processes ', Lithuanian Mathematical Journal, vol. 51, no. 3, pp. 342-361 . ResearcherID |
| Popis: | We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to a number of important families of processes that are not self-similar in the conventional sense. This includes a new class of fractional Hougaard motions defined as moving averages of Hougaard L\'evy process, as well as some well-known families of Hougaard L\'evy processes such as the Poisson processes, Brownian motions with drift, and the inverse Gaussian processes. Such families have many properties in common with ordinary self-similar processes, including the form of their covariance functions, and the fact that they appear as limits in a Lamperti-type limit theorem for families of stochastic processes. Comment: 23 pages. IMADA preprint 2010-09-01 |
| Databáze: | OpenAIRE |
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