Ebook: Stochastic Space—Time Models and Limit Theorems

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.

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Content:
Front Matter....Pages i-xi
Stochastic Space-Time Models and Limit Theorems: An Introduction....Pages 1-9
Markov Processes on Infinite Dimensional Spaces, Markov Fields and Markov Cosurfaces....Pages 11-40
Maximal Regularity for Stochastic Convolutions and Applications to Stochastic Evolution Equations in Hilbert Spaces....Pages 41-52
Stochastic Integration of Banach Space Valued Functions....Pages 53-79
A Semigroup Model for Parabolic Equations with Boundary and Pointwise Noise....Pages 81-94
On the Semigroup Approach to Stochastic Evolution Equations....Pages 95-139
Markovianization of Random Vibrations....Pages 141-162
Stochastic Analysis on Nuclear Spaces and its Applications....Pages 163-177
Stochastic Limit Theorems: Some Examples from Nonequilibrium Physics....Pages 179-189
On the Functional Limit Theorems....Pages 191-215
Tightness Of Sequences Of Hilbert Valued Martingales....Pages 217-226
Asymptotic Analysis of a Semi-Linear PDE with Wide-Band Noise Disturbances....Pages 227-242
A Central Limit Theorem for a System of Interacting Particles....Pages 243-248
Moments of States over Nuclear LSF Spaces....Pages 249-261
Back Matter....Pages 263-266

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Content:
Front Matter....Pages i-xi
Stochastic Space-Time Models and Limit Theorems: An Introduction....Pages 1-9
Markov Processes on Infinite Dimensional Spaces, Markov Fields and Markov Cosurfaces....Pages 11-40
Maximal Regularity for Stochastic Convolutions and Applications to Stochastic Evolution Equations in Hilbert Spaces....Pages 41-52
Stochastic Integration of Banach Space Valued Functions....Pages 53-79
A Semigroup Model for Parabolic Equations with Boundary and Pointwise Noise....Pages 81-94
On the Semigroup Approach to Stochastic Evolution Equations....Pages 95-139
Markovianization of Random Vibrations....Pages 141-162
Stochastic Analysis on Nuclear Spaces and its Applications....Pages 163-177
Stochastic Limit Theorems: Some Examples from Nonequilibrium Physics....Pages 179-189
On the Functional Limit Theorems....Pages 191-215
Tightness Of Sequences Of Hilbert Valued Martingales....Pages 217-226
Asymptotic Analysis of a Semi-Linear PDE with Wide-Band Noise Disturbances....Pages 227-242
A Central Limit Theorem for a System of Interacting Particles....Pages 243-248
Moments of States over Nuclear LSF Spaces....Pages 249-261
Back Matter....Pages 263-266
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