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Encompassing both introductory and more advanced research material, these notes deal with the author's contributions to stochastic processes and focus on Brownian motion processes and its derivative white noise.Originally published in 1970.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Stationary processes --- Stationary processes. --- Stochastic processes --- 519.216 --- 519.216 Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Bochner integral. --- Bochner's theorem. --- Bounded operator. --- Bounded variation. --- Brownian motion. --- Characteristic exponent. --- Characteristic function (probability theory). --- Complexification. --- Compound Poisson process. --- Computation. --- Conditional expectation. --- Continuous function (set theory). --- Continuous function. --- Continuous linear operator. --- Convergence of random variables. --- Coset. --- Covariance function. --- Cyclic subspace. --- Cylinder set. --- Degrees of freedom (statistics). --- Derivative. --- Differential equation. --- Dimension (vector space). --- Dirac delta function. --- Discrete spectrum. --- Distribution function. --- Dual space. --- Eigenfunction. --- Equation. --- Existential quantification. --- Exponential distribution. --- Exponential function. --- Finite difference. --- Fourier series. --- Fourier transform. --- Function (mathematics). --- Function space. --- Gaussian measure. --- Gaussian process. --- Harmonic analysis. --- Hermite polynomials. --- Hilbert space. --- Homeomorphism. --- Independence (probability theory). --- Independent and identically distributed random variables. --- Indicator function. --- Infinitesimal generator (stochastic processes). --- Integral equation. --- Isometry. --- Joint probability distribution. --- Langevin equation. --- Lebesgue measure. --- Lie algebra. --- Limit superior and limit inferior. --- Linear combination. --- Linear function. --- Linear interpolation. --- Linear subspace. --- Mean squared error. --- Measure (mathematics). --- Monotonic function. --- Normal distribution. --- Normal subgroup. --- Nuclear space. --- One-parameter group. --- Orthogonality. --- Orthogonalization. --- Parameter. --- Poisson point process. --- Polynomial. --- Probability distribution. --- Probability measure. --- Probability space. --- Probability. --- Projective linear group. --- Radon–Nikodym theorem. --- Random function. --- Random variable. --- Reproducing kernel Hilbert space. --- Self-adjoint operator. --- Self-adjoint. --- Semigroup. --- Shift operator. --- Special case. --- Stable process. --- Stationary process. --- Stochastic differential equation. --- Stochastic process. --- Stochastic. --- Subgroup. --- Summation. --- Symmetrization. --- Theorem. --- Transformation semigroup. --- Unitary operator. --- Unitary representation. --- Unitary transformation. --- Variance. --- White noise. --- Zero element.
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This volume includes papers by leading mathematicians in the fields of stochastic analysis, white noise theory and quantum information, together with their applications. The papers selected were presented at the International Conference on Stochastic Analysis: Classical and Quantum held at Meijo University, Nagoya, Japan from 1 to 5 November 2004. The large range of subjects covers the latest research in probability theory.
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Mathematical statistics --- Gauss [Processen van ] --- Gaussian processes --- Processus gaussiens
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Stochastic processes --- 51 --- Mathematics --- 51 Mathematics
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Chapter 1: Recognition and Teleportation (494 KB)
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White noise analysis is an advanced stochastic calculus that has developed extensively since three decades ago. It has two main characteristics. One is the notion of generalized white noise functionals, the introduction of which is oriented by the line of advanced analysis, and they have made much contribution to the fields in science enormously. The other characteristic is that the white noise analysis has an aspect of infinite dimensional harmonic analysis arising from the infinite dimensional rotation group. With the help of this rotation group, the white noise analysis has explored new are
White noise theory. --- Gaussian processes. --- Distribution (Probability theory) --- Stochastic processes --- White noise analysis --- Stochastic analysis
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The topics discussed in this book can be classified into three parts:. (i) Gaussian processes. 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. (ii) White noise analysis. This book includes the notes of the series of lectures 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 functionals", and sometimes "Hida distribution". (
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This volume constitutes the proceedings of the 3rd International Conference on Quantum Information. Topics covered include: quantum computation; NP-complete problem; quantum communication; quantum field theory; Gaussian random fields; complexity in nature; and more.
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