Theory of Stochastic Objects

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A01=Athanasios Christou Micheas
advanced probability concepts
Author_Athanasios Christou Micheas
Bernstein Von Mises Theorem
Borel Cantelli Lemma
Category=PBT
Category=PBTB
Category=PBWL
Cauchy Criterion
Conjugate Prior
convergence in stochastic processes
Convergent Subsequence
Cumulative Distribution Function
Data Augmentation
Distribution Functions
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Full Posterior Distribution
graduate level mathematics
Iid Random Variables
Iid Sequence
Inversion Theorem
measure theory applications
Mixture Models
MLE Estimator
Multivariate Gamma Function
Non-central Moments
Partial Sums
Polish Space
Posterior Distribution
Prior Distribution
Probability Measures
random
Random Objects
Random Variable
Random Vectors
statistical estimation methods
stochastic modeling techniques
unified framework for random objects
Weak Convergence

Product details

  • ISBN 9781466515208
  • Weight: 880g
  • Dimensions: 178 x 254mm
  • Publication Date: 24 Jan 2018
  • Publisher: Taylor & Francis Inc
  • Publication City/Country: US
  • Product Form: Hardback
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This book defines and investigates the concept of a random object. To accomplish this task in a natural way, it brings together three major areas; statistical inference, measure-theoretic probability theory and stochastic processes. This point of view has not been explored by existing textbooks; one would need material on real analysis, measure and probability theory, as well as stochastic processes - in addition to at least one text on statistics- to capture the detail and depth of material that has gone into this volume.

  • Presents and illustrates ‘random objects’ in different contexts, under a unified framework, starting with rudimentary results on random variables and random sequences, all the way up to stochastic partial differential equations.
  • Reviews rudimentary probability and introduces statistical inference, from basic to advanced, thus making the transition from basic statistical modeling and estimation to advanced topics more natural and concrete.
  • Compact and comprehensive presentation of the material that will be useful to a reader from the mathematics and statistical sciences, at any stage of their career, either as a graduate student, an instructor, or an academician conducting research and requiring quick references and examples to classic topics.
  • Includes 378 exercises, with the solutions manual available on the book's website.
  • 121 illustrative examples of the concepts presented in the text (many including multiple items in a single example).

The book is targeted towards students at the master’s and Ph.D. levels, as well as, academicians in the mathematics, statistics and related disciplines. Basic knowledge of calculus and matrix algebra is required. Prior knowledge of probability or measure theory is welcomed but not necessary.

Athanasios Christou Micheas is Associate Professor of Statistics at the University of Missouri.

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