Semi-Markov processes, integro-differential equations and anomalous diffusion-aggregation

DOI10.1214/20-AIHP1053zbMath1476.60161arXiv1807.07060OpenAlexW3093912648WikidataQ115240815 ScholiaQ115240815MaRDI QIDQ2028951

Bruno Toaldo, Mladen Svetoslavov Savov

Publication date: 3 June 2021

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.07060

zbMATH Keywords

integro-differential equationssemi-Markov processesadditive processessubordinatorsfractional equationstime-changed processes

Mathematics Subject Classification ID

Markov renewal processes, semi-Markov processes (60K15) Anomalous diffusion models (subdiffusion, superdiffusion, continuous-time random walks, etc.) (60K50)

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First passage times over stochastic boundaries for subdiffusive processes ⋮ Investigation of fractional order differential equation for boundary functional of a semi-Markov random walk process with negative drift and positive jumps ⋮ From semi-Markov random evolutions to scattering transport and superdiffusion ⋮ CTRW approximations for fractional equations with variable order ⋮ Random time-change with inverses of multivariate subordinators: governing equations and fractional dynamics ⋮ Convergence results for the time-changed fractional Ornstein–Uhlenbeck processes ⋮ Self-similar Cauchy problems and generalized Mittag-Leffler functions ⋮ Extinction time of non-Markovian self-similar processes, persistence, annihilation of jumps and the Fréchet distribution ⋮ Limit theorems for prices of options written on semi-Markov processes

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