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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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Book 6 in the Princeton Mathematical Series.Originally published in 1941.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.
Laplace transformation. --- Absolute continuity. --- Absolute convergence. --- Absolute value. --- Analytic continuation. --- Analytic function. --- Antiderivative. --- Arbitrarily large. --- Arithmetic progression. --- Asymptote. --- Auxiliary function. --- Bernstein polynomial. --- Bessel function. --- Big O notation. --- Bounded function. --- Bounded variation. --- Cauchy's theorem (group theory). --- Central limit theorem. --- Change of variables. --- Complex number. --- Conjugate transpose. --- Continuous function (set theory). --- Continuous function. --- Countable set. --- Derivative. --- Determinant. --- Differential operator. --- Dirichlet integral. --- Dirichlet series. --- Entire function. --- Equation. --- Euler's theorem. --- Existential quantification. --- Finite difference. --- Fubini's theorem. --- Function (mathematics). --- Generating function. --- Hamburger moment problem. --- Hausdorff moment problem. --- Helly–Bray theorem. --- Hölder's inequality. --- Imaginary number. --- Improper integral. --- Infimum and supremum. --- Integral equation. --- Integration by parts. --- Laguerre polynomials. --- Lambert series. --- Laplace transform. --- Laurent series. --- Lebesgue integration. --- Lebesgue–Stieltjes integration. --- Leibniz integral rule. --- Limit of a sequence. --- Limit point. --- Limit superior and limit inferior. --- Lipschitz continuity. --- Mathematical induction. --- Mean value theorem. --- Moment problem. --- Monotonic function. --- Multiple integral. --- Natural number. --- Order condition. --- Order of integration (calculus). --- Order of integration. --- Parseval's theorem. --- Plancherel theorem. --- Polynomial. --- Positive polynomial. --- Positive semidefinite. --- Power series. --- Prime factor. --- Prime number theorem. --- Prime number. --- Principal value. --- Radius of convergence. --- Representation theorem. --- Resultant. --- Riemann–Stieltjes integral. --- Right half-plane. --- Series (mathematics). --- Series expansion. --- Sign (mathematics). --- Simultaneous equations. --- Singular integral. --- Special case. --- Stieltjes moment problem. --- Stone–Weierstrass theorem. --- Summation. --- Taylor's theorem. --- Theorem. --- Total variation. --- Uniform continuity. --- Uniform convergence. --- Uniqueness theorem. --- Upper and lower bounds. --- Vanish at infinity. --- Variable (mathematics). --- Without loss of generality. --- Zero of a function.
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