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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

    $27.99 USD

  • 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

    $49.49 USD

  • 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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  • 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

    $49.49 USD

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  • Understanding Analysis

    Series series Mathematics and Statistics (R0)
    This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of ... Read more

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  • Brownian Motion and Stochastic Calculus

    Series series Mathematics and Statistics (R0)
    This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous ... Read more

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  • Short-Memory Linear Processes and Econometric Applications

    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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  • Foundations of Modern Analysis

    by J. Dieudonne ...
    In this text, the whole structure of analysis is built up from the foundations. The only things assumed at the outset are the rules of logic and the usual properties of the natural numbers, and with these two exceptions all the proofs in the text rest on the axioms and theorems proved earlier. Nevertheless this treatise (including the first volume) is not suitable for students who have not yet ... Read more

    $9.99 USD or Free with Kobo Plus

  • Zeta and q-Zeta Functions and Associated Series and Integrals

    Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory and applications of the basic (or q-) extensions of various special functions is included. This book ... Read more

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  • Backward Stochastic Differential Equations

    From Linear to Fully Nonlinear Theory

    Series series Mathematics and Statistics (R0)
    This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations ... Read more

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  • Singularly Perturbed Methods for Nonlinear Elliptic Problems

    Series series Cambridge Studies in Advanced Mathematics
    This introduction to the singularly perturbed methods in the nonlinear elliptic partial differential equations emphasises the existence and local uniqueness of solutions exhibiting concentration property. The authors avoid using sophisticated estimates and explain the main techniques by thoroughly investigating two relatively simple but typical non-compact elliptic problems. Each chapter then ... Read more

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  • Stochastic Differential Equations, Backward SDEs, Partial Differential Equations

    Series series Mathematics and Statistics (R0)
    This research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics. It pays special attention to the relations between SDEs/BSDEs and second order PDEs under minimal regularity assumptions, and also extends ... Read more

    $134.09 USD