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  • Functional Inequalities Markov Semigroups and Spectral Theory

    by Fengyu Wang ...
    Series series The Science Series of the Contemporary Elite Youth
    In this book, the functional inequalities are introduced to describe:(i) the spectrum of the generator: the essential and discrete spectrums, high order eigenvalues, the principle eigenvalue, and the spectral gap;(ii) the semigroup properties: the uniform intergrability, the compactness, the convergence rate, and the existence of density;(iii) the reference measure and the intrinsic metric: the ... Read more

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  • Foundation of Probability Theory

    This textbook presents measure theory in a concise yet clear manner, providing readers with a solid foundation in the mathematical axiomatic system of probability theory. Unlike elementary probability theory, which deals with random events through specific examples of random trials, Foundations of Probability Theory offers a comprehensive mathematical framework for rigorous descriptions of these ... Read more

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  • Distribution Dependent Stochastic Differential Equations

    Series Book 5 - World Scientific Series on Probability Theory and Its Applications
    Corresponding to the link of Itô's stochastic differential equations (SDEs) and linear parabolic equations, distribution dependent SDEs (DDSDEs) characterize nonlinear Fokker–Planck equations. This type of SDEs is named after McKean–Vlasov due to the pioneering work of H P McKean (1966), where an expectation dependent SDE is proposed to characterize nonlinear PDEs for Maxwellian gas. Moreover, by ... Read more

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  • Harnack Inequalities for Stochastic Partial Differential Equations

    by Feng-Yu Wang ...
    Series series Mathematics and Statistics (R0)
    In this book the author presents a self-contained account of Harnack inequalities and applications for the semigroup of solutions to stochastic partial and delayed differential equations. Since the semigroup refers to Fokker-Planck equations on infinite-dimensional spaces, the Harnack inequalities the author investigates are dimension-free. This is an essentially different point from the above ... Read more

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  • Analysis For Diffusion Processes On Riemannian Manifolds

    by Feng-yu Wang ...
    Series Book 18 - Advanced Series On Statistical Science And Applied Probability
    Stochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula ... Read more

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  • Integrated Treatment Technology of Rural Domestic Sewage

    Ten Cases of Integrated Sewage Treatment in Rural Area of China

    Series series Earth and Environmental Science (R0)
    This open access book provides integrated treatment technology of rural domestic sewage, and highlights ten typical cases in China. The integrated sewage treatment system (ISTE) combine sewage pretreatment, biological treatment, sedimentation, and disinfection, which particularly suitable for decentralized domestic wastewater treatment in rural areas without pipe networks. The main advantages of ... Read more

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    Edited by Ka-Sing Lau, De-Jun Feng ...
    Series series Springer Nature Proceedings excluding Computer Science
    This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held ... Read more

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    This book serves as a comprehensive source of asymptotic results for econometric models with deterministic exogenous regressors. Such regressors include linear (more generally, piece-wise polynomial) trends, seasonally oscillating functions, and slowly varying functions including logarithmic trends, as well as some specifications of spatial matrices in the theory of spatial models. The book begins ... Read more

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