PL
 |
EN
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 17

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last
Wyniki wyszukiwania
Wyszukiwano:
w słowach kluczowych:  weak convergence
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote Computation of solution of integral equations via fixed point results
Alqudah Manar A., Garodia Chanchal, Uddin Izhar, Nieto Juan J.
Demonstratio Mathematica
|
2022
|
Vol. 55, nr 1
772--785
EN
The motive of this article is to study a modified iteration scheme for monotone nonexpansive mappings in the class of uniformly convex Banach space and establish some convergence results. We obtain weak and strong convergence results. In addition, we present a nontrivial numerical example to show the convergence of our iteration scheme. To demonstrate the utility of our scheme, we discuss the solution of nonlinear integral equations as an application, which is again supported by a nontrivial example.
2
Content available remote Weak convergence of a numerical scheme for stochastic differential equations
Aguilera E., Fierro R.
Probability and Mathematical Statistics
|
2017
|
Vol. 37, Fasc. 1
201--215
EN
In this paper a numerical scheme approximating the solution to a stochastic differential equation is presented. On bounded subsets of time, this scheme has a finite state space, which allows us to decrease the round-off error when the algorithm is implemented. At the same time, the scheme introduced turns out locally consistent for any step size of time. Weak convergence of the scheme to the solution of the stochastic differentia equation is shown.
3
Content available Convergence Analysis of An Improved Extreme Learning Machine Based on Gradient Descent Method
Yusong L., Zhixun S., Bingjie Y., Xiaoling G., Zhaoyang S.
Journal of Applied Computer Science Methods
|
2016
|
Vol. 8 No. 1
5--15
EN
Extreme learning machine (ELM) is an efficient algorithm, but it requires more hidden nodes than the BP algorithms to reach the matched performance. Recently, an efficient learning algorithm, the upper-layer-solution-unaware algorithm (USUA), is proposed for the single-hidden layer feed-forward neural network. It needs less number of hidden nodes and testing time than ELM. In this paper, we mainly give the theoretical analysis for USUA. Theoretical results show that the error function monotonously decreases in the training procedure, the gradient of the error function with respect to weights tends to zero (the weak convergence), and the weight sequence goes to a fixed point (the strong convergence) when the iterations approach positive infinity. An illustrated simulation has been implemented on the MNIST database of handwritten digits which effectively verifies the theoretical results.
4
Content available remote A Wick functional limit theorem
Parczewski P.
Probability and Mathematical Statistics
|
2014
|
Vol. 34, Fasc. 1
127--145
EN
We prove that weak convergence of multivariate discrete Wiener integrals towards the continuous counterparts carries over to the application of discrete and continuous Wick calculus. This is done by the representation of arbitrary Wick products of Wiener integrals in terms of generalized Hermite polynomials and a discrete analog of the Hermite recursion. The result is a multivariate non-central limit theorem in the form of a Wick functional limit theorem. As an application we give approximations of multivariate processes based on fractional Brownian motions for arbitrary Hurst parameters H ∈ (0, 1).
5
Content available Weak convergence in L1 of the sequences of monotonic functions
Puchała P.
Journal of Applied Mathematics and Computational Mechanics
|
2014
|
Vol. 13, nr 3
195--199
EN
We use (quasi-) Young measures associated with strictly monotonic functions with a differentiable inverse to prove an L1 ([0,1],ℝ) weak convergence of the monotonic sequence of such functions. The result is well known, but the method seems to be new.
6
Content available remote Weak convergence for nonself nearly asymptotically nonexpansive mappings by iterations
Khan S. H.
Demonstratio Mathematica
|
2014
|
Vol. 47, nr 2
371--381
EN
In this paper, we obtain a couple of weak convergence results for nonself nearly asymptotically nonexpansive mappings. Our first result is for the Banach spaces satisfying Opial condition and the second for those whose dual satisfies the Kadec-Klee property.
7
Content available remote Selfsimilar processes with stationary increments in the second Wiener chaos
Maejima M., Tudor C. A.
Probability and Mathematical Statistics
|
2012
|
Vol. 32, Fasc. 1
167--186
EN
We study selfsimilar processes with stationary increments in the second Wiener chaos. We show that, in contrast with the first Wiener chaos which contains only one such process (the fractional Brownian motion), there is an infinity of selfsimilar processes with stationary increments living in the Wiener chaos of order two. We prove some limit theorems which provide a mechanism to construct such processes.
8
Content available Convergence theorems for strictly asymptotically pseudocontractive mappings in Hilbert spaces
Saluja G. S.
Opuscula Mathematica
|
2010
|
Vol. 30, no. 4
485-494
EN
In this paper, we establish the weak and strong convergence theorems for a k-strictly asymptotically pseudo-contractive mapping in the framework of Hilbert spaces. Our result improve and extend the corresponding result of Acedo and Xu, Liu, Marino and Xu, Osilike and Akuchu, and some others.
9
Content available remote Limit theorems for stochastic dynamical system arising in ising model analysis
Szwarc R., Topolski K.
Probability and Mathematical Statistics
|
2008
|
Vol. 28, Fasc. 2
257--270
EN
A simple stochastic dynamical system defined on the space of doubly-infinite sequences of real numbers is considered. Limit theorems for this system are proved. The results are applied to the physical model of wetting of the flat heterogeneous wall.
10
Content available remote A generalization of the Opial's theorem
Cegielski A.
Control and Cybernetics
|
2007
|
Vol. 36, no 3
601-610
EN
Opial presented in 1967 a theorem, which can be applied in order to prove the weak convergence of sequences (xk) in a Hilbert space, generated by iterative schemes of the form xk+1= Uxk for a nonexpansive and asymptotically regular operator U with nonempty Fix U. Several iterative schemes have, however, the form xk+i1 = UkXk, where (Uk) is a sequence of operators with a common fixed point. We show that under some conditions on the sequence (Uk) the sequence (xk) converges weakly to a common fixed point of operators Uk- We show also that the Opial's theorem and the Krasnoselskii-Mann theorem are the corollaries descending from the obtained results. Finally, we present some applications of the results to the convex feasibility problems.
11
Content available remote A note on the weak convergence of a sequence of successive approximations
Kalinde A., Mishra S., Singh S.
Demonstratio Mathematica
|
2006
|
Vol. 39, nr 3
619-624
EN
In this paper we discuss the weak convergence of the sequence of successive approximations for a generalized para-nonexpansive mapping in a reflexive Banach space that satisfies Opial's condition.
12
Content available remote Heavy-tailed dependent queues in heavy traffic
Szczotka W., Woyczyński W. A.
Probability and Mathematical Statistics
|
2004
|
Vol. 24, Fasc. 1
67--96
EN
The paper studies G/G/1 queues with heavy-tailed probability distributions of the service times and/or the interarrival times. It relies on the fact that the heavy traffic limiting distribution of the normalized stationary waiting times for such queues is equal to the distribution of the supremum M = sup0 ≤ t < ∞ (X(t)−βt), where X is a Lévy process. This distribution turns out to be exponential if the tail of the distribution of interarrival times is heavier than that of the service times, and it has a more complicated non-exponential shape in the opposite case; if the service times have heavy-tailed distribution in the domain of attraction of a one-sided α-stable distribution, then the limit distribution is Mittag-Leffler’s. In the case of a symmetric α-stable process X, the Laplace transform of the distribution of the supremum M is also given. Taking into account the known relationship between the heavy-traffic-regime distribution of queue length and its waiting time, asymptotic results for the former are also provided. Statistical dependence between the sequence of service times and the sequence of interarrival times, as well as between random variables within each of these two sequences, is allowed. Several examples are provided.
13
Content available remote Adaptive kernel estimation of the mode in a nonparametric random design regression model
Ziegler K.
Probability and Mathematical Statistics
|
2004
|
Vol. 24, Fasc. 2
213--235
EN
In a nonparametric regression model with random design, where the regression function m is given by m (x) = E(Y |X = x), estimation of the location θ (mode) and size m (θ) of a unique maximum of m is considered. As estimators, location θ and size m (θ) of a maximum of the Nadaraya-Watson kernel estimator m for the curve m are chosen. Within this setting, we establish joint asymptotic normality and asymptotic independence for θ and m (θ) (which can be exploited for constructing simultaneous confidence intervals for θ and m (θ)) under mild local smoothness assumptions on m and the design density g (imposed in a neighborhood of θ). The bandwidths employed for m are data-dependent and of plug-in type. This is handled by viewing the estimators as stochastic processes indexed by a so-called scaling parameter and proving functional central limit theorems for those processes. In the same way, we obtain, as a by-product, an asymptotic normality result for the Nadaraya-Watson estymator itself at a finite number of distinct points, which improves on previous results.
14
Content available remote On the restricted convergence of the intermediate and central terms of order statistics
Barakat H. M.
Probability and Mathematical Statistics
|
2003
|
Vol. 23, Fasc. 2
229--240
EN
As the distribution function (d.f.) of the suitably normalized general intermediate (or central) term of order statistics converges on an interval [c, d] to an arbitrary nondecreasing function, the continuation of this (weak) convergence on the whole real line to an intermediate (or central) value distribution is proved.
15
Content available remote Central limit theorem for a Gaussian incompressible flow with additional Brownian noise
Miernowski T.
Probability and Mathematical Statistics
|
2003
|
Vol. 23, Fasc. 2
413--434
EN
We generalize the result of Komorowski and Papanicolaou published in [7]. We consider the solution of stochastic differential equation dX (t) = V (t, X(t)) dt + √2κdB(t), where B(t) is a standard d-dimensional Brownian motion and V (t, x), (t, x) ∈ R × Rd, is a d-dimensional, incompressible, stationary, random Gaussian field decorrelating in finite time. We prove that the weak limit as ε ↓ 0 of the family of rescaled processes Xε(t) = εX(t/ε2) exists and may be identified as a certain Brownian motion.
16
Content available remote Conditioning and weak convergence
Jajte R., Paszkiewicz A.
Probability and Mathematical Statistics
|
1999
|
Vol. 19, Fasc. 2
453--461
EN
Several connections between the weak convergence of random variables, convergence of their distributions and conditioning have been described.
17
Multivariable regular variation of functions and measures
Meerschaert M. M., Scheffler H.-P.
Journal of Applied Analysis
|
1999
|
Vol. 5, nr 1
125-146
EN
Regular variation is an asymptotic property of functions and measures. The one variable theory is well-established, and has found numerous applications in both pure and applied mathematics. In this paper we present several new results on mul-tivariable regular variation for functions and measures.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.