On the convergence of quadratic variation for compound fractional Poisson processes

DOI10.2478/s13540-012-0023-2zbMath1278.60067OpenAlexW2083132043MaRDI QIDQ5327121

Noèlia Viles, Enrico Scalas

Publication date: 2 August 2013

Published in: Fractional Calculus and Applied Analysis (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/20.500.11824/571

zbMATH Keywords

continuous time random walkquadratic variationcompound renewal processinverse stable subordinatorfractional Poisson processMittag-Leffler waiting time\(M\)-Wright functions

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Fractional processes, including fractional Brownian motion (60G22) Fractional derivatives and integrals (26A33) Generalized stochastic processes (60G20) Mittag-Leffler functions and generalizations (33E12) Functional limit theorems; invariance principles (60F17)

Related Items

Fractional Skellam processes with applications to finance ⋮ Short note on the emergence of fractional kinetics ⋮ Optimal layer reinsurance for compound fractional Poisson model ⋮ The M-Wright function as a generalization of the Gaussian density for fractional diffusion processes

Uses Software

• mlrnd

Cites Work

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• The fractional Poisson process and the inverse stable subordinator
• The \(M\)-Wright function in time-fractional diffusion processes: a tutorial survey
• Fractional relaxation-oscillation and fractional diffusion-wave phenomena.
• A fractional generalization of the Poisson processes
• The multi-index Mittag-Leffler functions as an important class of special functions of fractional calculus
• The special functions of fractional calculus as generalized fractional calculus operators of some basic functions
• Fractional Poisson processes and related planar random motions
• Stochastic integration and \(L^ p-\)theory of semimartingales
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Fractional Poisson process
• Wright functions as scale-invariant solutions of the diffusion-wave equation
• Limit theorems for coupled continuous time random walks.
• Stochastic-Process Limits
• Nonlinear time-fractional differential equations in combustion science
• The fundamental solution of the space-time fractional diffusion equation
• REVISITING THE DERIVATION OF THE FRACTIONAL DIFFUSION EQUATION
• Limit theorems for continuous-time random walks with infinite mean waiting times
• The Asymptotic Expansion of the Generalized Bessel Function
• Weak Convergence of Stochastic Processes Defined on Semi-Infinite Time Intervals
• The Asymptotic Expansion of the Generalized Hypergeometric Function
• THE GENERALIZED BESSEL FUNCTION OF ORDER GREATER THAN ONE