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ON FOURIER COEFFICIENT ESTIMATORS CONSISTENT IN THE MEANSQUARE SENSE
"... Abstract. The properties of two recursive estimators of the Fourier coefficients of a regression function f ∈ L2[a, b] with respect to a complete orthonormal system of bounded functions (ek), k = 1, 2,..., are considered in the case of the observation model yi = f(xi) + ηi, i = 1,..., n, where ηi a ..."
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are independent random variables with zero mean and finite variance, xi ∈ [a, b] ⊂ R1, i = 1,..., n, form a random sample from a distribution with density % = 1/(b − a) (uniform distribution) and are independent of the errors ηi, i = 1,..., n. Unbiasedness and meansquare consistency of the examined estimators
The uniform meansquare ergodic theorem for wide sense stationary processes
 Stochastic Anal. Appl
, 1993
"... It is shown that the uniform meansquare ergodic theorem holds for the family of wide sense stationary sequences, as soon as the random process with orthogonal increments, which corresponds to the orthogonal stochastic measure generated by means of the spectral representation theorem, is of bounded ..."
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Cited by 2 (1 self)
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It is shown that the uniform meansquare ergodic theorem holds for the family of wide sense stationary sequences, as soon as the random process with orthogonal increments, which corresponds to the orthogonal stochastic measure generated by means of the spectral representation theorem, is of bounded
Meansquare convergence of stochastic multistep methods with variable stepsize
 J. Comput. Appl. Math
"... Abstract. We study meansquare consistency, stability in the meansquare sense and meansquare convergence of driftimplicit linear multistep methods with variable stepsize for the approximation of the solution of Itô stochastic differential equations. We obtain conditions that depend on the steps ..."
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Cited by 4 (3 self)
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Abstract. We study meansquare consistency, stability in the meansquare sense and meansquare convergence of driftimplicit linear multistep methods with variable stepsize for the approximation of the solution of Itô stochastic differential equations. We obtain conditions that depend on the step
Asymptotic meansquare stability of twostep methods for stochastic ordinary differential equations
 BIT Numerical Mathematics
"... We deal with linear multistep methods for SDEs and study when the numerical approximation shares asymptotic properties in the meansquare sense of the exact solution. As in deterministic numerical analysis we use a linear timeinvariant test equation and perform a linear stability analysis. Standar ..."
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Cited by 8 (1 self)
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We deal with linear multistep methods for SDEs and study when the numerical approximation shares asymptotic properties in the meansquare sense of the exact solution. As in deterministic numerical analysis we use a linear timeinvariant test equation and perform a linear stability analysis
Minimum meansquared error covariance shaping
 Hong Kong
, 2003
"... This paper develops and explores applications of a linear shaping transformation that minimizes the mean squared error (MSE) between the original and shaped data, i.e., that results in an output vector with the desired covariance that is as close as possible to the input, in an MSE sense. Three appl ..."
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Cited by 2 (2 self)
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This paper develops and explores applications of a linear shaping transformation that minimizes the mean squared error (MSE) between the original and shaped data, i.e., that results in an output vector with the desired covariance that is as close as possible to the input, in an MSE sense. Three
Series Expansion of WideSense Stationary Random Processes
"... AbsfracfThis paper presents a general approach to the derivation of series expansions of secondorder widesense stationary meansquare continuous random process valid over an infinitetime interval. The coefficients of the expansion are orthogonal and convergence is in the meansquare sense. The ..."
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Cited by 2 (0 self)
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AbsfracfThis paper presents a general approach to the derivation of series expansions of secondorder widesense stationary meansquare continuous random process valid over an infinitetime interval. The coefficients of the expansion are orthogonal and convergence is in the meansquare sense
xxxiii Competitive MeanSquared Error Beamforming
"... Abstract Beamforming methods are used extensively in a variety of different areas, where one of their main goals is to estimate the source signal amplitude s(t) from the array observations y(t) = s(t)a + i(t) + e(t), t = 1,2,..., where a is the steering vector, i(t) is the interference, and e(t) is ..."
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(t) is a Gaussian noise vector [1, 2]. To estimate s(t), we may use a beamformer with weights w so that s(t) = w*y(t), where s(t) is an estimate of s(t). To ensure that s(t) is close to s(t) in some sense, we may design the beamformer weights to minimize the MSE. However, since the MSE of a linear
Convergence Analysis of SemiImplicit Euler Methods for Solving Stochastic AgeDependent Capital System with Variable Delays and Random Jump Magnitudes
"... We consider semiimplicit Euler methods for stochastic agedependent capital system with variable delays and random jump magnitudes, and investigate the convergence of the numerical approximation. It is proved that the numerical approximate solutions converge to the analytical solutions in the mean ..."
Convergence of Analytical Stochastic Processes in Mean Square
"... In this paper we consider the random initial value classical problem Ẋ(t) = f(X(t), t), t ∈ T = [t0, t1], X(t0) = X0. We give, based on the Euler numerical approach, new and weaker conditions on f for its convergence in the mean square sense. This work also presents the process to build the numer ..."
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In this paper we consider the random initial value classical problem Ẋ(t) = f(X(t), t), t ∈ T = [t0, t1], X(t0) = X0. We give, based on the Euler numerical approach, new and weaker conditions on f for its convergence in the mean square sense. This work also presents the process to build
Nonlinear meansquare estimation with applications in remote sensing
 Proc. SPIE
, 1996
"... An approach to image modeling based on nonlinear meansquare estimation that does not assume a functio nal form for the model is described. The relationship between input and output images is represented in the form of a lookup table that can be efficiently computed from, and applied to images. Thre ..."
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Cited by 2 (1 self)
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An approach to image modeling based on nonlinear meansquare estimation that does not assume a functio nal form for the model is described. The relationship between input and output images is represented in the form of a lookup table that can be efficiently computed from, and applied to images
Results 1  10
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