This volume presents some of the most influential papers published by Rabi N. Bhattacharya, along with commentaries from international experts, demonstrating his knowledge, insight, and influence in the field of probability and its applications. For more than three decades, Bhattacharya has made significant contributions in areas ranging from theoretical statistics via analytical probability theory, Markov processes, and random dynamics to applied topics in statistics, economics, and geophysics. Selected reprints of Bhattacharya’s papers are divided into three sections: Modes of Approximation, Large Times for Markov Processes, and Stochastic Foundations in Applied Sciences. The accompanying articles by the contributing authors not only help to position his work in the context of other achievements, but also provide a unique assessment of the state of their individual fields, both historically and for the next generation of researchers.
Rabi N. Bhattacharya: Selected Papers will be a valuable resource for young researchers entering the diverse areas of study to which Bhattacharya has contributed. Established researchers will also appreciate this work as an account of both past and present developments and challenges for the future.
Зміст
Part I: Modes of Approximation.- Hall, Contributions of Rabi Bhattacharya to the Central Limit Theory and Normal Approximation.- Yoshida, Asymptotic Expansions for Stochastic Processes.- Shao, An Introduction to Normal Approximation.- Reprints.- Part II: Large Time Asymptotics for Markov Processes I: Diffusion.- Varadhan, Martingale Methods for the Central Limit Theorem.- Kurtz, Ergodicity and Central Limit Theorems for Markov Processes.- Reprints.- Part III: Large Time Asymptotics for Markov Processes II: Dynamical Systems and Iterated Maps.- Athreya, Dynamical Systems, IID Random Iterations, and Markov Chains.- Waymire, Random Dynamical Systems and Selected Works of Rabi Bhattacharya.- Reprints.- Part IV: Stochastic Foundations in Applied Sciences I: Economics.- Kamihigashi, Stachurski, Stability Analysis for Random Dynamical Systems in Economics.- Roy, Some Economic Applications of Recent Advances in Random Dynamical Systems.- Reprints.- Part V: Stochastic Foundations in Applied Sciences II: Geophysics.- Thomann, Waymire, Advection-Dispersion in Fluid Media and Selected Works of Rabi Bhattacharya.- Flandoli, Romito, Cascade Representations for the Navier-Stokes Equations.- Reprints.- Part VI: Stochastic Foundations in Applied Sciences III: Statistics.- Dryden, Le, Preston, Wood, Nonparametric Statistical Methods on Manifolds.- Huckemann, Hotz, Nonparametric Statistics on Manifolds and Beyond.- Reprints.
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