Path integral for the probability of the trajectories generated by fractional dynamics subject to Gaussian white noise

DOI10.1016/j.aml.2006.08.015zbMath1142.82013OpenAlexW2014401285MaRDI QIDQ2470548

Guy Jumaric

Publication date: 14 February 2008

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2006.08.015

zbMATH Keywords

stochastic differential equationpath integralfractional noiseRiemann-Liouville derivativefractional Taylor's series

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31)

Related Items (4)

Statistical analysis for stochastic systems including fractional derivatives ⋮ Stock exchange fractional dynamics defined as fractional exponential growth driven by (usual) Gaussian white noise. Application to fractional Black-Scholes equations ⋮ Derivation and solutions of some fractional Black-Scholes equations in coarse-grained space and time. Application to Merton's optimal portfolio ⋮ Solvability in Gevrey classes of some nonlinear fractional functional differential equations

Cites Work

• Stochastic analysis of the 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
• Information Theory and Statistical Mechanics
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