Malempati M. Rao

Bio: Malempati M. Rao is an academic researcher from University of California. The author has contributed to research in topics: Stochastic process & Conditional expectation. The author has an hindex of 17, co-authored 63 publications receiving 3218 citations. Previous affiliations of Malempati M. Rao include Carnegie Mellon University & Institute for Advanced Study.

Theory of Orlicz spaces

Abstract: A reference/text for mathematicians or students involved in analysis, differential equations, probability theory, and the study of integral operators where only Lebesgue spaces were used in the past. Updates and extends the pioneering work by Krasnosel'skii and Rutickii in their 1958 treatise on Orl

Applications Of Orlicz Spaces

Abstract: Introduction and background material nonsquare and von Neumann-Jordan constants normal structure and WCS coefficients Jung constants of Orlicz spaces packing in Orlicz spaces Fourier analysis in Orlicz spaces applications to prediction analysis applications to stochastic analysis nonlinear PDEs and Orlicz spaces miscellaneous applications.

Measure Theory and Integration

Abstract: Introduction and Preliminaries Measurability and Measures Measurable Functions Classical Integration Differentiation and Duality Product Measures and Integrals Nonabsolute Integration Capacity Theory and Integration The Lifting Theorem Topological Measures Some Complements and Applications Appendix References Index of Symbols and Notation Author Index Subject Index

Probability theory with applications

Abstract: Foundations.- Background Material and Preliminaries.- Independence and Strong Convergence.- Conditioning and Some Dependence Classes.- Analytical Theory.- Probability Distributions and Characteristic Functions.- Weak Limit Laws.- Applications.- Stopping Times, Martingales, and Convergence.- Limit Laws for Some Dependent Sequences.- A Glimpse of Stochastic Processes.

Conditional measures and applications

Abstract: THE CONCEPT OF CONDITIONING Introduction Conditional Probability Given a Partition Conditional Expectation: Elementary Case Conditioning with Densities Conditional Probability Spaces: First Steps Bibliographical Notes THE KOLMOGOROV FORMULATION AND ITS PROPERTIES Introduction of the General Concept Basic Properties of Conditional Expectations Conditional Probabilities in the General Case Remarks on the Inclusion of Previous Concepts Conditional Independence and Related Concepts Bibliographical Notes COMPUTATIONAL PROBLEMS ASSOCIATED WITH CONDITIONING Introduction Some Examples with Multiple Solutions: Paradoxes Dissection of Paradoxes Some Methods of Computation Remarks on Traditional Calculations of Conditional Measures Bibliographical Notes AN AXIOMATIC APPROACH TO CONDITIONAL PROBABILITY Introduction Axiomatization of Conditioning Based on Partitions Structure of the New Conditional Probability Functions Some Applications Difficulties with Earlier Examples Persist Bibliographical Notes REGULARITY OF CONDITIONAL MEASURES Introduction Existence of Regular Conditional Probabilities: Generalities Special Spaces Admitting Regular Conditional Probabilities Disintegration of Probability Measures and Regular Conditioning Further Results on Disintegration Evaluation of Conditional Expectations by Fourier Analysis Further Evaluations of Conditional Expectations Bibliographical Notes SUFFICIENCY Introduction Conditioning Relative to Families of Measures Sufficiency: The Dominated Case Sufficiency: The Undominated Case Sufficiency: Another Approach to the Undominated Case Bibliographical Notes ABSTRACTION OF KOLMOGOROV'S FORMULATION Introduction Integration Relative to Conditional Measures and Function Spaces Functional Characterizations of Conditioning Integral Representations of Conditional Expectations Renyi's Formulation as a Specialization of the Abstract Version Conditional Measures and Differentiation Bibliographical Notes PRODUCTS OF CONDITIONAL MEASURES Introduction A General Formulation of Products General Projective Limit Theorems Some Consequences Remarks on Conditioning, Disintegration, and Lifting Bibliographical Notes APPLICATIONS TO MARTINGALES AND MARKOV PROCESSES Introduction Set Martingales Martingale Convergence Markov Processes: Some Basic Results Further Properties of Markov Processes Bibliographical Notes APPLICATIONS TO MODERN ANALYSIS Introduction and Motivation Conditional Measures and Potential Kernels Reynolds Operators and Conditional Expectations Bistochastic Operators and Conditioning Contractive Projections and Conditional Expectations Bibliographical Notes CONDITIONING IN GENERAL STRUCTURES Introduction Averagings in Cones of Positive Functions Averaging Operators on Function Algebras Conditioning in Operator Algebras Free Independence and a Bijection in Operator Algebras Some Applications of Noncommutative Conditioning Bibliographical Notes REFERENCES NOTATIONS AUTHOR INDEX SUBJECT INDEX

One-Parameter Semigroups for Linear Evolution Equations

Abstract: Linear Dynamical Systems.- Semigroups, Generators, and Resolvents.- Perturbation and Approximation of Semigroups.- Spectral Theory for Semigroups and Generators.- Asymptotics of Semigroups.- Semigroups Everywhere.- A Brief History of the Exponential Function.

Sobolev met Poincaré

Abstract: Introduction What are Poincare and Sobolev inequalities? Poincare inequalities, pointwise estimates, and Sobolev classes Examples and necessary conditions Sobolev type inequalities by means of Riesz potentials Trudinger inequality A version of the Sobolev embedding theorem on spheres Rellich-Kondrachov Sobolev classes in John domains Poincare inequality: examples Carnot-Caratheodory spaces Graphs Applications to PDE and nonlinear potential theory Appendix References.

Cause and Correlation in Biology: A User's Guide to Path Analysis, Structural Equations and Causal Inference

Abstract: Many problems in biology require an understanding of the relationships among variables in a multivariate causal context. Exploring such cause-effect relationships through a series of statistical methods, this book explains how to test causal hypotheses when randomised experiments cannot be performed. This completely revised and updated edition features detailed explanations for carrying out statistical methods using the popular and freely available R statistical language. Sections on d-sep tests, latent constructs that are common in biology, missing values, phylogenetic constraints, and multilevel models are also an important feature of this new edition. Written for biologists and using a minimum of statistical jargon, the concept of testing multivariate causal hypotheses using structural equations and path analysis is demystified. Assuming only a basic understanding of statistical analysis, this new edition is a valuable resource for both students and practising biologists.

Weak and Measure-Valued Solutions to Evolutionary PDEs

Abstract: This book provides a concise treatment of the theory of nonlinear evolutionary partial differential equations. It provides a rigorous analysis of non-Newtonian fluids, and outlines its results for applications in physics, biology, and mechanical engineering