Talagrand concentration inequalities for stochastic heat-type equations under uniform distance

DOI10.1214/19-EJP388zbMath1427.60134MaRDI QIDQ2279324

Shijie Shang, Tu-Sheng Zhang

Publication date: 12 December 2019

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ejp/1573527858

zbMATH Keywords

stochastic partial differential equationsconcentration of measurestochastic heat equationstransportation cost inequalitiesmoment estimates for stochastic convolutions

Mathematics Subject Classification ID

Optimal stochastic control (93E20) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (10)

Transportation inequalities under uniform metric for a stochastic heat equation driven by time-white and space-colored noise ⋮ Talagrand’s quadratic transportation cost inequalities for SPDEs driven by fractional noises with two reflection walls ⋮ Talagrand's transportation inequality for SPDEs with locally monotone drifts ⋮ Transportation cost-information inequality for a stochastic heat equation driven by fractional-colored noise ⋮ Stochastic evolutionary \(p\)-Laplace equation: large deviation principles and transportation cost inequality ⋮ Global well-posedness to stochastic reaction-diffusion equations on the real line \(\mathbb{R}\) with superlinear drifts driven by multiplicative space-time white noise ⋮ A transportation inequality for reflected SPDEs on infinite spatial domain ⋮ Quadratic transportation cost inequality for scalar stochastic conservation laws ⋮ Transportation cost inequalities for stochastic reaction-diffusion equations with Lévy noises and non-Lipschitz reaction terms ⋮ Talagrand's quadratic transportation cost inequalities for reflected SPDEs driven by space-time white noise

Cites Work

• Characterization of Talagrand's transport-entropy inequalities in metric spaces
• Concentration inequalities and model selection. Ecole d'Eté de Probabilités de Saint-Flour XXXIII -- 2003.
• Heat kernel estimates for the Dirichlet fractional Laplacian
• Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
• Transportation inequalities for stochastic heat equations
• Global solutions to stochastic reaction-diffusion equations with super-linear drift and multiplicative noise
• Transportation cost-information inequalities and applications to random dynamical systems and diffusions.
• Concentration of measure and isoperimetric inequalities in product spaces
• A measure concentration inequality for contracting Markov chains
• Transportation cost for Gaussian and other product measures
• Concentration for multidimensional diffusions and their boundary local times
• Talagrand concentration inequalities for stochastic partial differential equations
• Concentration of measure for Brownian particle systems interacting through their ranks
• Bounding \(\bar d\)-distance by informational divergence: A method to prove measure concentration
• A note on transportation cost inequalities for diffusions with reflections
• Some inequalities for martingales and stochastic convolutions
• Semi Log-Concave Markov Diffusions
• Stochastic Equations in Infinite Dimensions
• Liquidity, Risk Measures, and Concentration of Measure
• Transportation Cost Inequalities for Diffusions Under Uniform Distance
• Concentration of Measure for the Analysis of Randomized Algorithms
• New concentration inequalities in product spaces
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