Stochastic applications of Caputo-type convolution operators with nonsingular kernels
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Publication:5880402
DOI10.1080/07362994.2021.2021091OpenAlexW4220876779MaRDI QIDQ5880402
Publication date: 9 March 2023
Published in: Stochastic Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2106.15972
compound Poisson processBernstein functionsPrabhakar functionrisk reserve processCaputo-like convolution operators
Processes with independent increments; Lévy processes (60G51) Fractional derivatives and integrals (26A33) Integro-differential operators (47G20) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)
Cites Work
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- General fractional calculus, evolution equations, and renewal processes
- Poisson-type processes governed by fractional and higher-order recursive differential equations
- Properties of the Caputo-Fabrizio fractional derivative and its distributional settings
- A comment on some new definitions of fractional derivative
- Alternative forms of compound fractional Poisson processes
- Random-time processes governed by differential equations of fractional distributed order
- On the long-range dependence of mixed fractional Poisson process
- A comment on a controversial issue: a generalized fractional derivative cannot have a regular kernel
- Why fractional derivatives with nonsingular kernels should not be used
- Analysis of a physically-relevant variable-order time-fractional reaction-diffusion model with Mittag-Leffler kernel
- A second order accurate approximation for fractional derivatives with singular and non-singular kernel applied to a HIV model
- Caputo-Fabrizio operator in terms of integer derivatives: memory or distributed lag?
- Convolution-type derivatives, hitting-times of subordinators and time-changed \(C_0\)-semigroups
- Fractional Poisson Process: Long-Range Dependence and Applications in Ruin Theory
- Lévy Processes and Stochastic Calculus
- Basic Theory
- General Fractional Derivatives
- Time-changed Poisson processes of order k
- Bernstein functions. Theory and applications