Description
Asymptotic behaviour of stochastic flows of diffeomorphisms.- Stochastic ensembles and hierarchies.- A stochastic approach to the minimum principle for the complex Monge-Ampère operator.- Construction of stochastic processes associated with the Boltzmann equation and its applications.- Isotropic stochastic flows and a related property of non-random potential flows.- Explosion problems for symmetric diffusion processes.- Extremal process as a substitution for "one-sided stable process with index 0".- Diffusion model of population genetics incorporating group selection, with special reference to an altruistic trait.- On laplacian operators of generalized brownian functionals.- Precise estimates for the fundamental solutions to some degenerate elliptic differential equations.- On stochastic algorithms in adaptive filtering.- Estimation theory and statistical physics.- Quantum stochastic calculus.- Quantum theory and stochastic processes - Some contact points.- The use of packing measure in the analysis of random sets. Kiyosi Itô was born on September 1915, in Kuwana, Japan. After his undergraduate and doctoral studies at Tokyo University, he was associate professor at Nagoya University before joining the faculty of Kyoto University in 1952. He has remained there ever since and is now Professor Emeritus, but has also spent several years at each of Stanford, Aarhus and Cornell Universities and the University of Minnesota. Itô's fundamental contributions to probability theory, especially the creation of stochastic differential and integral calculus and of excursion theory, form a cornerstone of this field. They have led to a profound understanding of the infinitesimal development of Markovian sample paths, and also of applied problems and phenomena associated with the planning, control and optimization of engineering and other random systems.
Contents
Asymptotic behaviour of stochastic flows of diffeomorphisms.- Stochastic ensembles and hierarchies.- A stochastic approach to the minimum principle for the complex Monge-Ampère operator.- Construction of stochastic processes associated with the Boltzmann equation and its applications.- Isotropic stochastic flows and a related property of non-random potential flows.- Explosion problems for symmetric diffusion processes.- Extremal process as a substitution for "one-sided stable process with index 0".- Diffusion model of population genetics incorporating group selection, with special reference to an altruistic trait.- On laplacian operators of generalized brownian functionals.- Precise estimates for the fundamental solutions to some degenerate elliptic differential equations.- On stochastic algorithms in adaptive filtering.- Estimation theory and statistical physics.- Quantum stochastic calculus.- Quantum theory and stochastic processes — Some contact points.- The use of packing measure in the analysis of random sets.
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