Parabolic type equations and Markov stochastic processes on adeles

DOI10.1007/s00041-013-9277-2zbMath1333.35126arXiv1206.5213OpenAlexW1973728648MaRDI QIDQ485175

Sergii M. Torba, Wilson A. Zuniga-Galindo

Publication date: 9 January 2015

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.5213

zbMATH Keywords

pseudodifferential operatorsparabolic equationsnon-Archimedean analysisadelesultrametricityheat kernels, Markov processes

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Abstract parabolic equations (35K90) PDEs with randomness, stochastic partial differential equations (35R60) Operator theory over fields other than (mathbb{R}), (mathbb{C}) or the quaternions; non-Archimedean operator theory (47S10) Initial value problems for PDEs with pseudodifferential operators (35S10) Heat kernel (35K08)

Related Items (15)

On a diffusion on finite adeles and the Feynman-Kac integral ⋮ Invariant ultrametrics and Markov processes on the finite adèle ring of \(\mathbb{Q}\) ⋮ \(p\)-adic mathematical physics: the first 30 years ⋮ Blow-up phenomena for \(p\)-adic semilinear heat equations ⋮ Ultrametric diffusion, exponential landscapes, and the first passage time problem ⋮ \(p\)-adic wavelets and their applications ⋮ Adelic multiresolution analysis, construction of wavelet bases and pseudo-differential operators ⋮ Heat Traces and Spectral Zeta Functions for $p$-adic Laplacians ⋮ The non-Archimedean stochastic heat equation driven by Gaussian noise ⋮ Nonlocal operators, parabolic-type equations, and ultrametric random walks ⋮ On infinitesimal generators and Feynman–Kac integrals of adelic diffusion ⋮ \(p\)-adic elliptic quadratic forms, parabolic-type pseudodifferential equations with variable coefficients and Markov processes ⋮ Pseudodifferential operators and Markov processes on adèles ⋮ \(p\)-adic analogue of the wave equation ⋮ A three gap theorem for adeles

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