Fractional multiple birth-death processes with birth probabilities \(\lambda _i(\Delta t)^\alpha +o((\Delta t)^\alpha)\)

DOI10.1016/j.jfranklin.2010.09.004zbMath1225.60141OpenAlexW1988408512MaRDI QIDQ621931

Guy Jumaric

Publication date: 31 January 2011

Published in: Journal of the Franklin Institute (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfranklin.2010.09.004

zbMATH Keywords

birth-death processesfractional Poissonian process

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Fractional derivatives and integrals (26A33) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Continuous-time Markov processes on discrete state spaces (60J27) Fractional ordinary differential equations (34A08)

Related Items (8)

Fractional randomness ⋮ Asymptotic behavior and quasi-limiting distributions on time-fractional birth and death processes ⋮ Use of squared magnitude function in approximation and hardware implementation of SISO fractional order system ⋮ Frequency boundary of fractional order systems with nonlinear uncertainties ⋮ Global attractivity for nonlinear fractional differential equations ⋮ Application of numerical inverse Laplace transform algorithms in fractional calculus ⋮ Robust stability and stabilization of fractional order interval systems with coupling relationships: the \(0<\alpha<1\) case ⋮ Robust stability analysis for a class of fractional order systems with uncertain parameters

Cites Work

• Unnamed Item
• Unnamed Item
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Stochastic analysis of the fractional Brownian motion
• Alternative micropulses and fractional Brownian motion
• Fractional Brownian motions via random walk in the complex plane and via fractional derivative. Comparison and further results on their Fokker-Planck equations
• A class of micropulses and antipersistent fractional Brownian motion
• Lagrangian mechanics of fractional order, Hamilton-Jacobi fractional PDE and Taylor's series of nondifferentiable functions
• Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable. functions. Further results
• On the representation of fractional Brownian motion as an integral with respect to \((dt)^a\)
• On the solution of the stochastic differential equation of exponential growth driven by fractional Brownian motion
• On linear birth-death processes with multiple births
• FRACTIONAL WHITE NOISE CALCULUS AND APPLICATIONS TO FINANCE
• Stochastic Calculus for Fractional Brownian Motion I. Theory
• Stochastic differential equations with fractional Brownian motion input
• A New Representation for Stochastic Integrals and Equations
• Fractional Brownian Motions, Fractional Noises and Applications
• Taylor’s Series Generalized for Fractional Derivatives and Applications
• On stochastic differential equations

This page was built for publication: Fractional multiple birth-death processes with birth probabilities \(\lambda _i(\Delta t)^\alpha +o((\Delta t)^\alpha)\)