## Rabi N. Bhattacharya: Selected PapersThis 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. |

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### Contents

Diffusion | 128 |

Dynamical Systems and Iterated Maps | 263 |

Economics | 362 |

Geophysics | 408 |

Statistics | 585 |

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### Common terms and phrases

analysis applications assume assumptions asymptotic expansion Athreya bootstrap Borel bounded Brownian motion central limit theorem coefficients compact confidence region constant converges in distribution Corollary defined denote density differentiable diffusion dispersion economic Edgeworth expansion embedding equation ergodic estimate Euclidean example exists exponential extrinsic sample mean finite follows Fourier Fréchet mean Gaussian geodesic given independent initial integral intrinsic mean iteration k-ads landmarks Lebesgue measure Lemma majorizing kernels Majumdar Markov chains Markov process martingale Math Mathematical Statistics mean set metric space models nonfocal normal approximation obtained parameter periodic positive probability measure proof Proposition Rabi Rabi Bhattacharya random dynamical systems random variables random vectors Remark result Riemannian manifold sample mean satisfying scale Section sequence shape spaces solution splitting condition Springer Stochastic Processes subset Theorem 2.1 theory transition probability unique invariant probability velocity Waymire zero