دانلود کتاب Selected papers of Takeyuki Hida

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This volume contains several surveys of important developments in quantum probability. The new type of quantum central limit theorems, based on the notion of free independence rather than the usual Boson or Fermion independence is discussed. A surprising result is that the role of the Gaussian for this new type of independence is played by the Wigner distribution. This motivated the introduction of new type of quantum independent increments noise, the free noise and the corresponding stochastic calculus. A further generalization, the q-noises, is discussed. The free stochastic calculus is shown to be able to fit naturally into the general representation free calculus. The basic free are shown to be realized as non-adapted stochastic integrals with respect to the usual Boson white noises. Quantum noise on the finite difference algebra is expressed in terms of the usual Boson white noises. A new quantum way of looking at classical stochastic flows, in particular diffusions on Riemannian Manifolds is explained. Quantum groups are discussed from the point of view of possible applications to quantum probability. The applications of quantum probability to physics are surveyed The topics discussed in this book can be classified into three parts: Gaussian processes; white noise analysis; and variational calculus for random fields. The most general and in fact final representation theory of Gaussian processes is included in this book. This theory is still referred to often and its developments are discussed. This book also includes the notes of the series of lectures on white noise analysis delivered in 1975 at Carleton University in Ottawa. They describe the very original idea of introducing the notion of generalized Brownian functionals (nowadays called "generalized white noise functions", and sometimes "Hida distribution"). The topic of variational calculus for random fields will certainly represnt one of the driving research lines for probability theory in the next century, as can be seen from several papers in this volume.  Read more... General theory of white noise functionals; Gaussian and other processes; infinite dimensional harmonic analysis and rotation group; quantum theory; Feynman integrals and random fields; variational calculus and random fields; application to biology