共查询到20条相似文献,搜索用时 46 毫秒
1.
Abstract We study multiple Riemann-Stieltjes integral approximations to multiple Stratonovich fractional integrals. Two standard approximations (Wong-Zakai and Mollifier approximations) are considered and we show the convergence in the mean square sense and uniformly on compact time intervals of these approximations to the multiple Stratonovich fractional integral. 相似文献
2.
XiaoMingWANG WangZHOU 《数学学报(英文版)》2004,20(1):93-104
The authors establish the approximations to the distribution of M-estimates in a linear model by the bootstrap and the linear representation of bootstrap M-estimation,and prove that the approximation is valid in probability 1.A simulation is made to show the effects of bootstrap approximation,randomly weighted approximation and normal approximation. 相似文献
3.
In this paper, we consider lightweight decentralised algorithms for achieving consensus in distributed systems. Each member of a distributed group has a private value from a fixed set consisting of, say, two elements, and the goal is for all members to reach consensus on the majority value. We explore variants of the voter model applied to this problem. In the voter model, each node polls a randomly chosen group member and adopts its value. The process is repeated until consensus is reached. We generalise this so that each member polls a (deterministic or random) number of other group members and changes opinion only if a suitably defined super-majority has a different opinion. We show that this modification greatly speeds up the convergence of the algorithm, as well as substantially reducing the probability of it reaching consensus on the incorrect value. 相似文献
4.
AbstractIn this article, we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existing fully explicit space-time discrete approximation scheme, in particular the fact that it satisfies suitable a priori estimates. We also obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the article to the stochastic Burgers equations with additive space-time white noise. 相似文献
5.
In this paper, we shall establish transcendence measures of several numbers with good approximations by algebraic numbers. This generalizes the results of Caveny (Proc. Amer. Math. Soc.
120 (1994) 349–357) and Tubbs (Proc. Amer. Math. Soc.
109 (1990) 297–304), and gives a quantitative version of Ably's result (C.R. Acad. Sci. Paris
1(313), série I (1991) 653–655). 相似文献
6.
K. Ziȩtak 《Journal of Computational and Applied Mathematics》1984,11(3):297-305
In this paper we investigate a connection between lp-approximation and the Chebyshev approximation of a rectangular matrix by matrices of smaller rank. We consider also the stationary points of problems (4) and (5) which are connected with these approximations. 相似文献
7.
Asymptotic results for weighted means of linear combinations of independent Poisson random variables
Rita Giuliano Claudio Macci 《Stochastics An International Journal of Probability and Stochastic Processes》2020,92(4):497-518
ABSTRACT In this paper we prove the large deviation principle for a class of weighted means of linear combinations of independent Poisson distributed random variables, which converge weakly to a normal distribution. The interest in these linear combinations is motivated by the diffusion approximation in Lansky [On approximations of Stein's neuronal model, J. Theoret. Biol. 107 (1984), pp. 631–647] of the Stein's neuronal model (see Stein [A theoretical analysis of neuronal variability, Biophys. J. 5 (1965), pp. 173–194]). We also prove an analogue result for sequences of multivariate random variables based on the diffusion approximation in Tamborrino, Sacerdote, and Jacobsen [Weak convergence of marked point processes generated by crossings of multivariate jump processes. Applications to neural network modeling, Phys. D 288 (2014), pp. 45–52]. The weighted means studied in this paper generalize the logarithmic means. We also investigate moderate deviations. 相似文献
8.
José C. Pinheiro Douglas M. Bates 《Journal of computational and graphical statistics》2013,22(1):12-35
Abstract Nonlinear mixed-effects models have received a great deal of attention in the statistical literature in recent years because of the flexibility they offer in handling the unbalanced repeated-measures data that arise in different areas of investigation, such as pharmacokinetics and economics. Several different methods for estimating the parameters in nonlinear mixed-effects model have been proposed. We concentrate here on two of them—maximum likelihood and restricted maximum likelihood. A rather complex numerical issue for (restricted) maximum likelihood estimation in nonlinear mixed-effects models is the evaluation of the log-likelihood function of the data, because it involves the evaluation of a multiple integral that, in most cases, does not have a closed-form expression. We consider here four different approximations to the log-likelihood, comparing their computational and statistical properties. We conclude that the linear mixed-effects (LME) approximation suggested by Lindstrom and Bates, the Laplacian approximation, and Gaussian quadrature centered at the conditional modes of the random effects are quite accurate and computationally efficient. Gaussian quadrature centered at the expected value of the random effects is quite inaccurate for a smaller number of abscissas and computationally inefficient for a larger number of abscissas. Importance sampling is accurate, but quite inefficient computationally. 相似文献
9.
Cartoon-like images, i.e., C2 functions which are smooth apart from a C2 discontinuity curve, have by now become a standard model for measuring sparse (nonlinear) approximation properties of directional representation systems. It was already shown that curvelets, contourlets, as well as shearlets do exhibit sparse approximations within this model, which are optimal up to a log-factor. However, all those results are only applicable to band-limited generators, whereas, in particular, spatially compactly supported generators are of uttermost importance for applications.In this paper, we present the first complete proof of optimally sparse approximations of cartoon-like images by using a particular class of directional representation systems, which indeed consists of compactly supported elements. This class will be chosen as a subset of (non-tight) shearlet frames with shearlet generators having compact support and satisfying some weak directional vanishing moment conditions. 相似文献
10.
Abstract In this article, we study a continuous time optimal filter and its various numerical approximations. This filter arises in an optimal allocation problem in the particular context of a non-stationary economy. We analyse the rates of convergence of the approximations of the filter when the model is misspecified and when the observations can only be made at discrete times. We give bounds that are uniform in time. Numerical results are presented. 相似文献
11.
Toshiyuki Nakayama 《随机分析与应用》2013,31(5):832-857
ABSTRACTThe goal of this paper is to prove a convergence rate for Wong–Zakai approximations of semilinear stochastic partial differential equations driven by a finite-dimensional Brownian motion. Several examples, including the HJMM equation from mathematical finance, illustrate our result. 相似文献
12.
In this paper we show that Uspensky's expansion theorem for the Poisson approximation of the distribution of sums of independent Bernoulli random variables can be rewritten in terms of the Poisson convolution semigroup. This gives rise to exact evaluations and simple remainder term estimations for the deviations of the distributions in study with respect to various probability metrics, generalizing results of Shorgin (1977, Theory Probab. Appl., 22, 846–850). Finally, we compare the sharpness of Poisson versus normal approximations. 相似文献
13.
We apply a Bayesian approach to the problem of prediction in an unbalanced growth curve model using noninformative priors. Due to the complexity of the model, no analytic forms of the predictive densities are available. We propose both approximations and a prediction-oriented Metropolis-Hastings sampling algorithm for two types of prediction, namely the prediction of future observations for a new subject and the prediction of future values for a partially observed subject. They are illustrated and compared through real data and simulation studies. Two of the approximations compare favorably with the approximation in Fearn (1975, Biometrika, 62, 89–100) and are very comparable to the more accurate Rao-Blackwellization from Metropolis-Hastings sampling algorithm. 相似文献
14.
Carole Bernard 《Applied Mathematical Finance》2013,20(2):140-173
AbstractWe study the fair strike of a discrete variance swap for a general time-homogeneous stochastic volatility model. In the special cases of Heston, Hull–White and Schöbel–Zhu stochastic volatility models, we give simple explicit expressions (improving Broadie and Jain (2008a). The effect of jumps and discrete sampling on volatility and variance swaps. International Journal of Theoretical and Applied Finance, 11(8), 761–797) in the case of the Heston model). We give conditions on parameters under which the fair strike of a discrete variance swap is higher or lower than that of the continuous variance swap. The interest rate and the correlation between the underlying price and its volatility are key elements in this analysis. We derive asymptotics for the discrete variance swaps and compare our results with those of Broadie and Jain (2008a. The effect of jumps and discrete sampling on volatility and variance swaps. International Journal of Theoretical and Applied Finance, 11(8), 761–797), Jarrow et al. (2013. Discretely sampled variance and volatility swaps versus their continuous approximations. Finance and Stochastics, 17(2), 305–324) and Keller-Ressel and Griessler (2012. Convex order of discrete, continuous and predictable quadratic variation and applications to options on variance. Working paper. Retrieved from http://arxiv.org/abs/1103.2310). 相似文献
15.
Bayes estimation in a mixture inverse Gaussian model 总被引:1,自引:0,他引:1
Ramesh C. Gupta H. Olcay Akman 《Annals of the Institute of Statistical Mathematics》1995,47(3):493-503
In this paper a mixture model involving the inverse Gaussian distribution and its length biased version is studied from a Bayesian view-point. Using proper priors, the Bayes estimates of the parameters of the model are derived and the results are applied on the aircraft data of Proschan (1963,Technometrics,5, 375–383). The posterior distributions of the parameters are expressed in terms of the confluent-hypergeometric function and the modified Bessel function of the third kind. The integral involved in the expression of the estimate of the mean is evaluated by numerical techniques. 相似文献
16.
Numerical approximation of the boundary control for the wave equation with mixed finite elements in a square 总被引:1,自引:0,他引:1
17.
In this paper we consider the M
t queueing model with infinitely many servers and a nonhomogeneous Poisson arrival process. Our goal is to obtain useful insights
and formulas for nonstationary finite-server systems that commonly arise in practice. Here we are primarily concerned with
the peak congestion. For the infinite-server model, we focus on the maximum value of the mean number of busy servers and the
time lag between when this maximum occurs and the time that the maximum arrival rate occurs. We describe the asymptotic behavior
of these quantities as the arrival changes more slowly, obtaining refinements of previous simple approximations. In addition
to providing improved approximations, these refinements indicate when the simple approximations should perform well. We obtain
an approximate time-dependent distribution for the number of customers in service in associated finite-server models by using
the modified-offered-load (MOL) approximation, which is the finite-server steady-state distribution with the infinite-server
mean serving as the offered load. We compare the value and lag in peak congestion predicted by the MOL approximation with
exact values for M
t/M/s delay models with sinusoidal arrival-rate functions obtained by numerically solving the Chapman–Kolmogorov forward equations.
The MOL approximation is remarkably accurate when the delay probability is suitably small. To treat systems with slowly varying
arrival rates, we suggest focusing on the form of the arrival-rate function near its peak, in particular, on its second and
third derivatives at the peak. We suggest estimating these derivatives from data by fitting a quadratic or cubic polynomial
in a suitable interval about the peak.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
18.
A new approach to the approximation of operators in the Hilbert space of functions on a locally compact Abelian (LCA) group is developed. This approach is based on sampling the symbols of such operators. To choose the points for sampling, we use the approximations of LCA groups by finite groups, which were introduced and investigated by Gordon. In the case of the group R
n
, the constructed approximations include the finite-dimensional approximations of the coordinate and linear momentum operators, suggested by Schwinger. The finite-dimensional approximations of the Schrödinger operator based on Schwinger's approximations were considered by Digernes, Varadarajan, and Varadhan in Rev. Math. Phys. 6 (4) (1994), 621–648 where the convergence of eigenvectors and eigenvalues of the approximating operators to those of the Schrödinger operator was proved in the case of a positive potential increasing at infinity. Here this result is extended to the case of Schrödinger-type operators in the Hilbert space of functions on LCA groups. We consider the approximations of p-adic Schrödinger operators as an example. For the investigation of the constructed approximations, the methods of nonstandard analysis are used. 相似文献
19.
《Numerical Functional Analysis & Optimization》2013,34(4-5):565-575
ABSTRACT The paper discusses common fixed point theory for generalized I-contractions of Ciric and R-subweakly commuting maps. Various results on invariant approximations are obtained. 相似文献