Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years – due mainly to the impetus of the authors and their collaborators – a powerful connection has been established between stochastic geometry and the Malliavin calculus of variations, which is a collection of probabilistic techniques based on the properties of infinite-dimensional differential operators. This has led in particular to the discovery of a large number of new quantitative limit theorems for high-dimensional geometric objects. This unique book presents an organic collection of authoritative surveys written by the principal actors in this rapidly evolving field, offering a rigorous yet lively presentation of its many facets.

Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Polytopes. --- Probabilities. --- Combinatorics. --- Probability Theory and Stochastic Processes. --- Applications of Mathematics. --- Stochastic analysis. --- Poisson processes. --- Processes, Poisson --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes --- Point processes --- Distribution (Probability theory. --- Math --- Science --- Combinatorics --- Algebra --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Engineering --- Engineering analysis --- Hyperspace --- Topology --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

"The purpose of this monograph is to discuss recent developments in the analysis of isotropic spherical random fields, with a view towards applications in Cosmology.We shall be concerned in particular with the interplay among three leading themes, namely: - the connection between isotropy, representation of compact groups and spectral analysis for random fields, including the characterization of polyspectra and their statistical estimation - the interplay between Gaussianity, Gaussian subordination, nonlinear statistics, and recent developments in the methods of moments and diagram formulae to establish weak convergence results - the various facets of high-resolution asymptotics, including the high-frequency behaviour of Gaussian subordinated random fields and asymptotic statistics in the high-frequency sense"--

Spherical harmonics. --- Random fields. --- Compact groups. --- Cosmology --- Astronomy --- Deism --- Metaphysics --- Groups, Compact --- Locally compact groups --- Topological groups --- Fields, Random --- Stochastic processes --- Functions, Potential --- Potential functions --- Harmonic analysis --- Harmonic functions --- Statistical methods.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The concept of Wiener chaos generalizes to an infinite-dimensional setting the properties of orthogonal polynomials associated with probability distributions on the real line. It plays a crucial role in modern probability theory, with applications ranging from Malliavin calculus to stochastic differential equations and from probabilistic approximations to mathematical finance. This book is concerned with combinatorial structures arising from the study of chaotic random variables related to infinitely divisible random measures. The combinatorial structures involved are those of partitions of finite sets, over which Möbius functions and related inversion formulae are defined. This combinatorial standpoint (which is originally due to Rota and Wallstrom) provides an ideal framework for diagrams, which are graphical devices used to compute moments and cumulants of random variables. Several applications are described, in particular, recent limit theorems for chaotic random variables. An Appendix presents a computer implementation in MATHEMATICA for many of the formulae.

Operational research. Game theory --- Discrete mathematics --- Mathematical physics --- differentiaalvergelijkingen --- chaos --- discrete wiskunde --- stochastische analyse --- kansrekening