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951.
The aim of the paper is to present a new approach to the theory of functional integral equations of fractional order. That approach depends on converting of the mentioned equations to the form of functional integral equations of Volterra-Stieltjes type. It turns out that the study of functional integral equations of Volterra-Stieltjes type is more convenient and effective than the study of functional integral equations of fractional order. An example illustrating our approach is also discussed. 相似文献
952.
Won-Gil Park 《Journal of Mathematical Analysis and Applications》2011,376(1):193-202
In this paper, we investigate approximate additive mappings, approximate Jensen mappings and approximate quadratic mappings in 2-Banach spaces. That is, we prove the generalized Hyers-Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces. 相似文献
953.
Qidi Peng 《Statistics & probability letters》2011,81(8):1326-1335
Let {X(t)}t∈R be a stationary increments Gaussian process satisfying some assumptions. By using the notion of generalized quadratic variation we build a strongly consistent and asymptotically normal estimator of the uniform Hölder exponent of X, over a compact interval. Our estimator is obtained starting from average values of the process over a regular grid. 相似文献
954.
955.
本文对混合约束极大极小问题的目标函数与约束分别用熵函数来逼近,讨论了逼近问题的二次规划子问题的搜索方向的显式形式,并给出了极大极小问题和多目标规划的二次规划予问题的显式解。将所得结果用于相应的算法中,可提高算法的有效性。 相似文献
956.
957.
Michael R. Osborne Brett Presnell Berwin A. Turlach 《Journal of computational and graphical statistics》2013,22(2):319-337
Abstract Proposed by Tibshirani, the least absolute shrinkage and selection operator (LASSO) estimates a vector of regression coefficients by minimizing the residual sum of squares subject to a constraint on the l 1-norm of the coefficient vector. The LASSO estimator typically has one or more zero elements and thus shares characteristics of both shrinkage estimation and variable selection. In this article we treat the LASSO as a convex programming problem and derive its dual. Consideration of the primal and dual problems together leads to important new insights into the characteristics of the LASSO estimator and to an improved method for estimating its covariance matrix. Using these results we also develop an efficient algorithm for computing LASSO estimates which is usable even in cases where the number of regressors exceeds the number of observations. An S-Plus library based on this algorithm is available from StatLib. 相似文献
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Given a Brownian Motion W, in this paper we study the asymptotic behavior, as ε→0, of the quadratic covariation between f(εW) and W in the case in which f is not smooth. Among the main features discovered is that the speed of the decay in the case f∈Cα is at least polynomial in ε and not exponential as expected. We use a recent representation as a backward–forward Itô integral of [f(εW),W] to prove an ε-dependent approximation scheme which is of independent interest. We get the result by providing estimates to this approximation. The results are then adapted and applied to generalize the results of Almada Monter and Bakhtin (2011) and Bakhtin (2011) related to the small noise exit from a domain problem for the saddle case. 相似文献