Pseudoprocesses Related to Space-Fractional Higher-Order Heat-Type Equations

DOI10.1080/07362994.2014.911107zbMath1312.60121arXiv1305.6409OpenAlexW2014148973MaRDI QIDQ2875520

Bruno Toaldo, Enzo Orsingher

Publication date: 8 August 2014

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.6409

zbMATH Keywords

stable processessubordinatorscontinuous-time random walksRiesz derivativespseudoprocessesFeller fractional operatorsWeyl derivatives

Mathematics Subject Classification ID

Special processes (60K99) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (8)

On fractional calculus of \(\mathcal A_{2n+1}(x)\) function ⋮ An Analogue of the Feynman--Kac Formula for a High-Order Operator ⋮ Symmetric \(\alpha\)-stable distributions with noninteger \(\alpha > 2\) and related stochastic processes ⋮ Probabilistic Representation of a Solution of the Cauchy Problem for Evolution Equations with Riemann--Liouville Operators ⋮ On Mellin transforms of solutions of differential equation \(\chi^{(n)}(x)+\gamma_nx\chi (x)=0\) ⋮ Estimates for functionals of solutions to higher-order heat-type equations with random initial conditions ⋮ Probabilistic representation formula for the solution of fractional high-order heat-type equations ⋮ On the generalized mass transfer with a chemical reaction: Fractional derivative model

Cites Work

• Probabilistic representation of fundamental solutions to \(\frac{\partial u}{\partial t} = \kappa _m \frac{\partial^m u}{\partial x^m}\)
• Distributions of sojourn time, maximum and minimum for pseudo-processes governed by higher-order heat-type equations
• On the solutions of linear odd-order heat-type equations with random initial conditions
• Asymptotic behaviour of the fundamental solution to ∂ u /∂ t = — ( — ∆) ^m u
• Fractional kinetic equations: solutions and applications
• Generalized Measures in Function Spaces
• An extension of certain quasi-measure

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