In this paper we consider stochastic recursive equations of sum type, X =(D) Sigma(K)(i-1) A(i)X(i) + b, and of max type, X =(D) max{A(i)X(i) + b(i) : l <= i <= k}, where A(i), b(i), and b are random, (X-i) are ...
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In this paper we consider stochastic recursive equations of sum type, X =(D) Sigma(K)(i-1) A(i)X(i) + b, and of max type, X =(D) max{A(i)X(i) + b(i) : l <= i <= k}, where A(i), b(i), and b are random, (X-i) are independent, identically distributed copies of X, and '=(D)' denotes equality in distribution. Equations of these types typically characterize limits in the probabilistic analysis of algorithms, in combinatorial optimization problems, and in many other problems having a recursive structure. We develop some new contraction properties of minimal L-s-metrics which allow us to establish general existence and uniqueness results for solutions without imposing any moment conditions. As an application we obtain a one-to-one relationship between the set of solutions to the homogeneous equation and the set of solutions to the inhomogeneous equation, for sum- and max-type equations. We also give a stochastic interpretation of a recent transfer principle of Rosler from nonnegative solutions of sum type to those of max type, by means of random scaled Weibull distributions.
作者：
Flammang, ValerieUniv Lorraine
UMR CNRS 7502 IECL Dept MathUFR MIM 3 Rue Augustin FresnelBP 45112 F-57073 Metz 3 France
Let a be a nonzero algebraic integer of degree d whose all conjugates alpha(1) = alpha, alpha(2), ..., alpha(d) vertical bar aeg z vertical bar <= theta, 0 <= theta <= 90 degrees. We define the N-measure of a...
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Let a be a nonzero algebraic integer of degree d whose all conjugates alpha(1) = alpha, alpha(2), ..., alpha(d) vertical bar aeg z vertical bar <= theta, 0 <= theta <= 90 degrees. We define the N-measure of a by N(alpha) - Pi(d)(i=1)(vertical bar alpha(i)vertical bar + 1/vertical bar alpha(i)vertical bar) and the absolute N-measure of alpha by v(alpha) = N(alpha)(1/deg(alpha)). Firstly, we consider the case theta = 0. We prove that N(alpha) is an element of N and that, if alpha is a reciprocal algebraic integer, N(alpha) is a square. Then, we study the set Ai of the quantities v(alpha). We prove that there exists a number 1 such that Ai is dense in (l, infinity). Finally, using the method of auxiliary functions, we find the seven smallest points of N in (2, l). In case of 0 < theta < 90 degrees, we compute the greatest lower bound c(theta) of the absolute N-measure of alpha, for alpha belonging to eight subintervals of ]0, theta [. Among these subintervals, two are complete. These computations are also done by using auxiliary functions. The polynomials involved in the auxiliary functions are found by our recursive algorithm.
Consider the D-optimal designs for a combined polynomial and trigonometric regression on a partial circle. It is shown that the optimal design is equally supported and the structure of the optimal design depends only ...
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Consider the D-optimal designs for a combined polynomial and trigonometric regression on a partial circle. It is shown that the optimal design is equally supported and the structure of the optimal design depends only on the length of the design interval and the support points are analytic functions of this parameter. Moreover, the Taylor expansion of the optimal support points can be determined efficiently by a recursive procedure. Examples are presented to illustrate the procedures for computing the optimal designs. (C) 2013 Elsevier B.V. All rights reserved.
A method utilizing single channel recordings to blindly separate the multicomponents overlapped in time and frequency domains is proposed in this paper. Based on the time varying AR model, the instantaneous frequency ...
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A method utilizing single channel recordings to blindly separate the multicomponents overlapped in time and frequency domains is proposed in this paper. Based on the time varying AR model, the instantaneous frequency and amplitude of each signal component are estimated respectively, thus the signal component separation is achieved. By using prolate spheroidal sequence as basis functions to expand the time varying parameters of the AR model, the method turns the problem of linear time varying parameters estimation to a linear time invariant parameter estimation problem, then the parameters are estimated by a recursive algorithm. The computation of this method is simple, and no prior knowledge of the signals is needed. Simulation results demonstrate validity and excellent performance of this method.
An extension of a hierarchical model of automaton programs is proposed. New elements help shorten the transition graphs of automata, without complicating the logic of automata-based programs.
An extension of a hierarchical model of automaton programs is proposed. New elements help shorten the transition graphs of automata, without complicating the logic of automata-based programs.
Recently, it has been discovered that symbolic algebraic manipulations can be performed on the computer with input/output data in symbolic form. Accordingly, and for slightly nonlinear two-point boundary-value problem...
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Recently, it has been discovered that symbolic algebraic manipulations can be performed on the computer with input/output data in symbolic form. Accordingly, and for slightly nonlinear two-point boundary-value problems, it is feasible to obtain approximate analytical solutions in the form of power series in a small parameter. In these solutions, the boundary values are presented in a literal form. In this paper, the Lie canonical transformation is applied to derive approximate optimal solutions for slightly nonlinear systems with quadratic criteria. The transformation generator is determined by simple partial differential equations of the first order. To determine the arbitrary constants of the transformation in terms of the two-point boundary values, inversion of a vectorial power series in a small parameter is required, and a recursive algorithm for this inversion is given. To express the final solution in terms of these boundary values, a substitution of the inverted vectorial power series into another vectorial power series is also necessary, and a recursive algorithm for this substitution is presented.
The stochastic Newton recursive algorithm is studied and utilized for identifying the dual-rate model which is derived through the polynomial transformation technique. The main advantage of the algorithm is that it ha...
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The stochastic Newton recursive algorithm is studied and utilized for identifying the dual-rate model which is derived through the polynomial transformation technique. The main advantage of the algorithm is that it has the extensive form and may earn more possible convergence properties with flexible parameters. The primary problem is that the sample covariance matrix may be singular when encountering numbers of model parameters and (or) no general input signal, which hinders the identification process. Thus, the main contribution is adding one symmetric positive definite matrix to the recursion of the sample covariance matrix. This simple approach solves the problem effectively. Two improved stochastic Newton recursive algorithms are then proposed for time-invariant and time-varying systems. The consistent and bounded convergence conclusions of the corresponding algorithms are drawn respectively. The final illustrative examples demonstrate the effectiveness and the convergence properties of the recursive algorithms.
A novel analytical design method for highly selective digital optimal equiripple comb finite-impulse response (FIR) filters is presented. The equiripple comb FIR filters are optimal in the Chebyshev sense. The number ...
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A novel analytical design method for highly selective digital optimal equiripple comb finite-impulse response (FIR) filters is presented. The equiripple comb FIR filters are optimal in the Chebyshev sense. The number of notch bands, the width of the notch bands and the attenuation in the passbands can be independently specified. The degree formula and the differential equation for the generating polynomial of the filter is presented. Based on the differential equation, a fast simple algebraic recursive procedure for the evaluation of the impulse response of the filter is described. Its arithmetic robustness outperforms, by far, the known analytical design method. Highly selective equiripple comb FIR filters with thousands of coefficients can be designed. One example demonstrates the efficiency of the filter design.
Two examples of filter equations are derived for which the measurement equation yields the directional cosine of the target relative to a known axis. This redefinition of the measurement equation leads to filter equat...
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Two examples of filter equations are derived for which the measurement equation yields the directional cosine of the target relative to a known axis. This redefinition of the measurement equation leads to filter equations which are nonlinear algebraic rather than transcendental. Furthermore, these equations are inherently three-dimensional. It is noted that inclusion of multiple measurement axes is straightforward. (L.M.)
We describe an extension of the recursive algorithm of Howard (1972) and Krailo and Pike (1984) for computation of conditional maximum likelihood estimates in multiple logistic regression models for stratum-matched re...
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We describe an extension of the recursive algorithm of Howard (1972) and Krailo and Pike (1984) for computation of conditional maximum likelihood estimates in multiple logistic regression models for stratum-matched retrospective studies to the multivariate case involving polytomous disease states. APL procedures, suitable for a desktop computing environment, are provided and analyzed.
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