A BROWNIAN-TIME EXCURSION INTO FOURTH-ORDER PDES, LINEARIZED KURAMOTO–SIVASHINSKY, AND BTP-SPDES ON ℝ+ × ℝd

DOI10.1142/S0219493706001864zbMath1109.60054MaRDI QIDQ3426806

Hassan Allouba

Publication date: 13 March 2007

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

zbMATH Keywords

Brownian-time processesfourth-order SPDEsfree propagatorBTP-PDEslinearized Kuramoto-Sivashinsky process

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Probabilistic potential theory (60J45) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Transition functions, generators and resolvents (60J35) Initial value problems for higher-order parabolic equations (35K30)

Related Items (8)

Variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation ⋮ 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 ⋮ INTERACTING TIME-FRACTIONAL AND Δ^ν PDES SYSTEMS VIA BROWNIAN-TIME AND INVERSE-STABLE-LÉVY-TIME BROWNIAN SHEETS ⋮ L-Kuramoto-Sivashinsky SPDEs vs. time-fractional SPIDEs: exact continuity and gradient moduli, 1/2-derivative criticality, and laws ⋮ Long time behavior for stochastic Burgers equations with jump noises ⋮ Moderate deviations for fourth-order stochastic heat equations with fractional noises ⋮ From Brownian-Time Brownian Sheet to a Fourth Order and a Kuramoto–Sivashinsky-Variant Interacting PDEs Systems

Cites Work

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• Laws of the iterated logarithm for \(\alpha\)-time Brownian motion
• 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.
• The Brownian snake and solutions of \(\Delta u = u^ 2\) in a domain
• Determining nodes for the Kuramoto-Sivashinsky equation
• The exit distribution for iterated Brownian motion in cones
• Brownian-time processes: The PDE connection II and the corresponding Feynman-Kac formula
• On the non-homogeneous stationary Kuramoto-Sivashinsky equation

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