Modern Probability Theory Solutions 3rd Edition Bhat.zip
probability theory plays a central role in modern statistics and applications. indeed, the theory has been at the core of many revolutionary advances in statistical inference, such as markov chain monte carlo sampling, variational inference, frequentist statistics, and methods for inference for complex models that combine ideas from several statistical disciplines, such as mixture models, graphical models, and latent variable models.
modern probability theory solutions 3rd edition bhat.zip
describes the basic notions and basic theorems from classical probability theory, with a focus on the central limit theorem, including the law of large numbers, the strong law of large numbers, the law of iterated logarithm, the lindeberg-feller central limit theorem, the lindeberg-gine-cantelli central limit theorem, and asymptotic normality. the main topics include: (1) the martingale central limit theorem, (2) the martingale central limit theorem for functions of independent random variables, (3) the martingale central limit theorem for sequences of independent random variables, (4) the martingale central limit theorem for weakly dependent random variables, (5) the strong martingale central limit theorem, and (6) markov chains and finite state markov chains. the book also contains some applications of these theorems, including a discussion of a random walk, the binomial distribution, the poisson distribution, and the exponential distribution.
probability theory on metric spaces was introduced in the last decades of the 20th century, following the great success of the theory on euclidean spaces. we will develop a general framework that allows to deal with probability problems in metric spaces. we will be concerned with the theory of borel random measures, markov random fields and martingales in metric spaces. as applications, we will discuss the dependence of the law of the iterated logarithm of a markov random walk in the time interval [0,1], and the decoupling problem for random fields and martingales in metric spaces.
