Stochastic Space--Time Models and Limit Theorems

ISBN-13: 9789401088794 / Angielski / Miękka / 2011 / 266 str.

L. Arnold; P. Kotelenez

Opis

Approach your problems from It isn't that they can't see the right end and begin with the solution. the answers. Then one day, It is that they can't see the perhaps you will find the problem. final question. G.K. Chesterton. The Scandal 'The Hermit Clad 1n Crane of Father Brown 'The Point of Feathers' in R. van Gulik's a Pin'. The Chinese Maze Murders. Growing specialisation and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches wich were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD" , "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Spis treści

Stochastic Space-Time Models and Limit Theorems: An Introduction.- I: Stochastic Analysis in Infinite Dimensions.- Markov Processes on Infinite Dimensional Spaces, Markov Fields and Markov Cosurfaces.- Maximal Regularity for Stochastic Convolutions and Applications to Stochastic Evolution Equations in Hilbert Spaces.- Stochastic Integration of Banach Space Valued Functions.- A Semigroup Model for Parabolic Equations with Boundary and Pointwise Noise.- On the Semigroup Approach to Stochastic Evolution Equations.- Markovianization of Random Vibrations.- Stochastic Analysis on Nuclear Spaces and its Applications.- II. Limit Theorems.- Stochastic Limit Theorems: Some Examples from Nonequilibrium Physics.- On the Functional Limit Theorems.- Tightness of Sequences of Hilbert Valued Martingales.- Asymptotic Analysis of a Semi-Linear PDE with Wide-Band Noise Disturbances.- A Central Limit Theorem for a System of Interacting Particles.- Moments of States over Nuclear LSF Spaces.