Random rewards, fractional Brownian local times and stable self-similar processes

DOI10.1214/105051606000000277zbMath1133.60016arXivmath/0610272OpenAlexW3101174273MaRDI QIDQ862213

Gennady Samorodnitsky, Serge Cohen

Publication date: 5 February 2007

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0610272

zbMATH Keywords

fractional Brownian motionintegral representationlocal timelong memorystationary processchaos expansionstable processself-similar processconservative flownull flowrandom rewardsuperposition of scaled inputs

Mathematics Subject Classification ID

Sample path properties (60G17) Self-similar stochastic processes (60G18) Stable stochastic processes (60G52)

Related Items (16)

Choquet random sup-measures with aggregations ⋮ Random walks at random times: convergence to iterated Lévy motion, fractional stable motions, and other self-similar processes ⋮ Discrete approximation of a stable self-similar stationary increments process ⋮ Ergodic properties of sum- and max-stable stationary random fields via null and positive group actions ⋮ On \(1/f\) noise ⋮ Functional central limit theorem for heavy tailed stationary infinitely divisible processes generated by conservative flows ⋮ Fractals in trade duration: capturing long-range dependence and heavy tailedness in modeling trade duration ⋮ Self-similar stochastic processes with stationary increments as limits of particle systems ⋮ Maxima of stable random fields, nonsingular actions and finitely generated abelian groups: a survey ⋮ Random-time isotropic fractional stable fields ⋮ Ruin probability with certain stationary stable claims generated by conservative flows ⋮ Maximal moments and uniform modulus of continuity for stable random fields ⋮ Stable random fields indexed by finitely generated free groups ⋮ A class of asymptotically self-similar stable processes with stationary increments ⋮ Simulation of a Local Time Fractional Stable Motion ⋮ Exceedance of power barriers for integrated continuous-time stationary ergodic stable processes

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