INTERACTING TIME-FRACTIONAL AND Δν PDES SYSTEMS VIA BROWNIAN-TIME AND INVERSE-STABLE-LÉVY-TIME BROWNIAN SHEETS

DOI10.1142/S0219493712500128zbMath1286.60070arXiv1105.0652OpenAlexW2963830986MaRDI QIDQ4908346

Erkan Nane, Hassan Allouba

Publication date: 5 March 2013

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.0652

zbMATH Keywords

random fieldsBrownian-time processesBrownian-time Feynman-Kac formulaiterated Brownian sheetBrownian-time Brownian sheetinitially perturbed fourth-order PDEslinear systems of fourth-order interacting PDEslinear systems of fractional interacting PDEslinear systems of high-order interacting PDEsmemory-preserving PDEs

Mathematics Subject Classification ID

Random fields (60G60) Brownian motion (60J65) Integral representations of solutions to PDEs (35C15) Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes (60J60) Probabilistic potential theory (60J45) Transition functions, generators and resolvents (60J35) Initial-boundary value problems for nonlinear higher-order PDEs (35G31) Initial-boundary value problems for systems of linear higher-order PDEs (35G46)

Related Items (7)

Time-inhomogeneous jump processes and variable order operators ⋮ Variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation ⋮ Time-Changed Processes Governed by Space-Time Fractional Telegraph Equations ⋮ Time dependent random fields on spherical non-homogeneous surfaces ⋮ Time-fractional and memoryful \(\Delta^{2^{k}}\) SIEs on \(\mathbb{R}_{+}\times\mathbb{R}^{d}\): how far can we push white noise? ⋮ L-Kuramoto-Sivashinsky SPDEs in one-to-three dimensions: L-KS kernel, sharp Hölder regularity, and Swift-Hohenberg law equivalence ⋮ L-Kuramoto-Sivashinsky SPDEs vs. time-fractional SPIDEs: exact continuity and gradient moduli, 1/2-derivative criticality, and laws

Cites Work

• Unnamed Item
• Composition of stochastic processes governed by higher-order parabolic and hyperbolic equations
• Fractional diffusion equations and processes with randomly varying time
• Iterated elastic Brownian motions and fractional diffusion equations
• Probabilistic construction of the solution of some higher order parabolic differential equation
• A linearized Kuramoto-Sivashinsky PDE via an imaginary-Brownian-time-Brownian-angle process
• Iterated Brownian motion in an open set.
• Fractional Cauchy problems on bounded domains
• The exit distribution for iterated Brownian motion in cones
• From Brownian-Time Brownian Sheet to a Fourth Order and a Kuramoto–Sivashinsky-Variant Interacting PDEs Systems
• Brownian-time processes: The PDE connection II and the corresponding Feynman-Kac formula
• A BROWNIAN-TIME EXCURSION INTO FOURTH-ORDER PDES, LINEARIZED KURAMOTO–SIVASHINSKY, AND BTP-SPDES ON ℝ₊ × ℝ^d
• Brownian subordinators and fractional Cauchy problems
• Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers
• Limit theorems for continuous-time random walks with infinite mean waiting times
• Lévy Processes and Stochastic Calculus
• STOCHASTIC SOLUTIONS OF A CLASS OF HIGHER ORDER CAUCHY PROBLEMS IN ℝ^d
• Higher order PDE’s and iterated processes

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