Probabilistic representation formula for the solution of fractional high-order heat-type equations
From MaRDI portal
Publication:2000975
DOI10.1007/s00028-019-00485-wzbMath1419.35201arXiv1611.03364OpenAlexW2963243045MaRDI QIDQ2000975
Sonia Mazzucchi, Stefano Bonaccorsi, Mirko D'Ovidio
Publication date: 1 July 2019
Published in: Journal of Evolution Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1611.03364
Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Integral representations of solutions to PDEs (35C15) Generalized stochastic processes (60G20) Fractional partial differential equations (35R11)
Related Items (3)
Fractional equations via convergence of forms ⋮ A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders ⋮ Space-time duality for semi-fractional diffusions
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Cauchy problems for fractional differential equations with Riemann-Liouville fractional derivatives
- From Sturm-Liouville problems to fractional and anomalous diffusions
- On the fractional counterpart of the higher-order equations
- On a connection between powers of operators and fractional Cauchy problems
- Fractional powers of closed operators and the semigroups generated by them
- Fractional kinetic equation for Hamiltonian chaos
- Fractional diffusion equations and processes with randomly varying time
- Probabilistic construction of the solution of some higher order parabolic differential equation
- A signed measure on path space related to Wiener measure
- Processes governed by signed measures connected with third-order ``heat- type equations
- The arc-sine law and its analogs for processes governed by signed and complex measures
- An asymptotically 4-stable process
- Conditional maximal distributions of processes related to higher-order heat-type equations
- Distributions of sojourn time, maximum and minimum for pseudo-processes governed by higher-order heat-type equations
- Brownian-time processes: The PDE connection and the half-derivative generator
- Iterated Brownian motion in an open set.
- Monopoles and dipoles in biharmonic pseudo process
- Fractal dimension results for continuous time random walks
- Fractional Cauchy problems on bounded domains
- Higher-order Laplace equations and hyper-Cauchy distributions
- An Itô calculus for a class of limit processes arising from random walks on the complex plane
- From pseudorandom walk to pseudo-Brownian motion: first exit time from a one-sided or a two-sided interval
- High order heat-type equations and random walks on the complex plane
- On the generation of semigroups of linear operators
- A signed measure on rough paths associated to a PDE of high order: results and conjectures
- A unified approach to infinite-dimensional integration
- Pseudoprocesses Related to Space-Fractional Higher-Order Heat-Type Equations
- Fractional diffusion and wave equations
- Brownian-time processes: The PDE connection II and the corresponding Feynman-Kac formula
- Brownian subordinators and fractional Cauchy problems
- Functional Integration and Partial Differential Equations. (AM-109)
- The fractional diffusion equation
- On some properties of fractional powers of linear operators
- Fractional diffusion equation on fractals: one-dimensional case and asymptotic behaviour
- Limit theorems for continuous-time random walks with infinite mean waiting times
- Fractional Calculus: Integral and Differential Equations of Fractional Order
- Inverse Stable Subordinators
- Higher order PDE’s and iterated processes
- Higher order Grünwald approximations of fractional derivatives and fractional powers of operators
- Generalized Measures in Function Spaces
- Fractional powers of closed operators
- On Distributions of Certain Wiener Functionals
- Diffusion Equation and Stochastic Processes
- Bernstein functions. Theory and applications
- Fractional powers of operators
- Boundary conditions for one-dimensional biharmonic pseudo process
- Projective limits of complex measures and martingale convergence
- On sojourn distributions of processes related to some higher-order heat-type equations
This page was built for publication: Probabilistic representation formula for the solution of fractional high-order heat-type equations