TY - BOOK ID - 8209688 TI - Lectures on Gaussian processes PY - 2012 SN - 3642249388 3642249396 9786613576958 1280399031 PB - Heidelberg : Springer, DB - UniCat KW - Gaussian processes. KW - Gaussian processes KW - Mathematics KW - Physical Sciences & Mathematics KW - Mathematical Statistics KW - Gaussian measures. KW - Isoperimetric inequalities. KW - Large deviations. KW - Deviations, Large KW - Measures, Gaussian KW - Mathematics. KW - Probabilities. KW - Probability Theory and Stochastic Processes. KW - Probability KW - Statistical inference KW - Combinations KW - Chance KW - Least squares KW - Mathematical statistics KW - Risk KW - Math KW - Science KW - Limit theorems (Probability theory) KW - Statistics KW - Geometry, Plane KW - Inequalities (Mathematics) KW - Measure theory KW - Distribution (Probability theory) KW - Stochastic processes KW - Distribution (Probability theory. KW - Distribution functions KW - Frequency distribution KW - Characteristic functions KW - Probabilities UR - https://www.unicat.be/uniCat?func=search&query=sysid:8209688 AB - Gaussian processes can be viewed as a far-reaching infinite-dimensional extension of classical normal random variables. Their theory presents a powerful range of tools for probabilistic modelling in various academic and technical domains such as Statistics, Forecasting, Finance, Information Transmission, Machine Learning - to mention just a few. The objective of these Briefs is to present a quick and condensed treatment of the core theory that a reader must understand in order to make his own independent contributions. The primary intended readership are PhD/Masters students and researchers working in pure or applied mathematics. The first chapters introduce essentials of the classical theory of Gaussian processes and measures with the core notions of reproducing kernel, integral representation, isoperimetric property, large deviation principle. The brevity being a priority for teaching and learning purposes, certain technical details and proofs are omitted. The later chapters touch important recent issues not sufficiently reflected in the literature, such as small deviations, expansions, and quantization of processes. In university teaching, one can build a one-semester advanced course upon these Briefs. ER -