Homogenization of nonlocal partial differential equations related to stochastic differential equations with Lévy noise

DOI10.3150/21-BEJ1365zbMath1504.60100arXiv1804.06555OpenAlexW4224310739WikidataQ114038747 ScholiaQ114038747MaRDI QIDQ2137035

Qiao Huang, Renming Song, Jin-qiao Duan

Publication date: 16 May 2022

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.06555

zbMATH Keywords

homogenizationFeynman-Kac formulaFeller semigroupsSDEs with jumpsstrong well-posednessZvonkin's transformnon-local parabolic PDEs

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Diffusion processes (60J60) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (4)

The Smoluchowski-Kramers limits of stochastic differential equations with irregular coefficients ⋮ Homogenization of non-symmetric jump processes ⋮ Weak averaging principle for multiscale stochastic dynamical systems driven by stable processes ⋮ Fast-slow stochastic dynamical system with singular coefficients

Cites Work

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• Yamada-Watanabe results for stochastic differential equations with jumps
• Homogenization of a singular random one-dimensional PDE with time-varying coefficients
• Pathwise uniqueness for singular SDEs driven by stable processes
• The implicit function theorem. History, theory, and applications
• Regularity results for stable-like operators
• Homogenization of cadlag processes
• The scaling limit behaviour of periodic stable-like processes
• Ergodicity and exponential \(\beta\)-mixing bounds for multidimensional diffusions with jumps
• Strong solutions to stochastic hydrodynamical systems with multiplicative noise of jump type
• Homogenization of periodic diffusion with small jumps
• Homogenization of periodic linear degenerate PDEs
• Homogenization of certain one-dimensional discontinuous Markov processes
• Homogenization of reticulated structures
• Elliptic partial differential equations of second order
• Heat kernels for time-dependent non-symmetric stable-like operators
• Asymptotic expansion formulas for functionals of \(\varepsilon\)-Markov processes with a mixing property
• Homogenization of linear and semilinear second order parabolic PDEs with periodic coefficients: A probabilistic approach
• On the Poisson equation and diffusion approximation. I
• Stochastic differential equations, backward SDEs, partial differential equations
• A functional non-central limit theorem for jump-diffusions with periodic coefficients driven by stable Lévy-noise
• Norms and determinants of linear mappings
• Heat kernel estimates for critical fractional diffusion operators
• Fluctuations in the homogenization of semilinear equations with random potentials
• Periodic Homogenization of Nonlocal Operators with a Convolution-Type Kernel
• Equivalence of Stochastic Equations and Martingale Problems
• Critical Homogenization of SDEs Driven by a Levy Process in Random Medium
• Lévy Processes and Stochastic Calculus
• Homogenization of a Class of Integro-Differential Equations with Lévy Operators
• Asymptotic Statistics
• One-Parameter Semigroups for Linear Evolution Equations
• Stochastic Homogenization of Linear Elliptic Equations: Higher-Order Error Estimates in Weak Norms Via Second-Order Correctors
• Multiscale Finite Element Methods for Advection-Dominated Problems in Perforated Domains
• Periodic Homogenization for Nonlinear Integro-Differential Equations
• Homogenization of Lévy-type Operators with Oscillating Coefficients
• Homogenization of a semilinear parabolic PDE with locally periodic coefficients: a probabilistic approach
• Shape optimization by the homogenization method
• A TRANSFORMATION OF THE PHASE SPACE OF A DIFFUSION PROCESS THAT REMOVES THE DRIFT

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