共查询到20条相似文献,搜索用时 31 毫秒
1.
K. Marton 《Probability Theory and Related Fields》1981,56(3):317-327
Summary For the class of discrete memoryless stationary correlated sources with non-singular dependence and maximal correlation less than 1, it is shown that two such sources can be isomorphic only if there exists a single letter isomorphism between them, and they can have only trivial isomorphisms. 相似文献
2.
K. Marton 《Israel Journal of Mathematics》1987,58(3):288-304
Let {(X
i,Z
i)} be an i.i.d. sequence of random pairs in a finite set × x ℒ; we will call it a discrete memoryless stationary correlated
(DMSC) source with generic distribution dist(X
1,Z
1). Two DMSC sources {(X
i,Z
i)} and {(X
i′,Z
i′)} are called asymptotically isomorphic in the weak sense if for every ε>0 and sufficiently largen, there exists a joint distribution dist(X
n,Z
n,X′
n,Z′
n) ofn-length blocks of the two sources such that
. For single sources of equal entropy, McMillan’s theorem implies asymptotic isomorphy in the sense suggested by this definition.
For correlated sources, however, no nontrivial cases of weak asymptotic isomorphy are known. We show that some spectral properties
of the generic distributions are invariant for weak asymptotic isomorphy, and these properties wholly determine the generic
distribution in many cases. 相似文献
3.
The set of correlated equilibria for a bimatrix game is a closed, bounded, convex set containing the set of Nash equilibria. We show that every extreme point of a maximal Nash set is an extreme point of the above convex set. We also give an example to show that this result is not true in the payoff space, i.e. there are games where no Nash equilibrium payoff is an extreme point of the set of correlated equilibrium payoffs. 相似文献
4.
Generating correlated Poisson random variables is fundamental in many applications in the management and engineering fields, and in many others where multivariate count data arise. Multivariate Poisson data are often approximately simulated by either independent univariate Poisson or multivariate Normal data, whose implementation is provided by the most common statistical software packages such as R . However, such simulated data are often not satisfactory. Alternatively, methods for simulating multivariate Poisson data can be used, but they are adversely affected by limitations ranging from computational complexity to restrictions on the correlation matrix, which dramatically reduce their practical applicability. In this work, we propose a new method that is highly accurate and computationally efficient and can be usefully employed even by non‐expert users in generating correlated Poisson data (and, more generally, any discrete variable), with assigned marginal distributions and correlation matrix. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
5.
Herwig Bruneel 《Operations Research Letters》1984,3(3):149-152
The letter considers a discrete buffered system with one randomly interrupted output channel and stochastic interruptions of the arrival stream which are correlated to the output interruptions. The behaviour of this buffer system is studied, and in particular the influence of the correlation is derived. 相似文献
6.
A ring is of finite type if it has only finitely many maximal right ideals, all two-sided. In this article, we give a complete set of invariants for finite direct sums of cyclically presented modules over a ring R of finite type. More generally, our results apply to finite direct sums of direct summands of cyclically presented right R-modules (DCP modules). Using a duality, we obtain as an application a similar set of invariants for kernels of morphisms between finite direct sums of pair-wise non-isomorphic indecomposable injective modules over an arbitrary ring. This application motivates the study of DCP modules. 相似文献
7.
Rudolf Ahlswede 《Probability Theory and Related Fields》1973,25(3):239-252
In this article we study a channel with arbitrarily varying channel probability functions in the presence of a noiseless feedback channel (a.v.ch.f.). We determine its capacity by proving a coding theorem and its strong converse. Our proof of the coding theorem is constructive; we give explicitly a coding scheme which performs at any rate below the capacity with an arbitrarily small decoding error probability. The proof makes use of a new method ([1]) to prove the coding theorem for discrete memoryless channels with noiseless feedback (d.m.c.f.). It was emphasized in [1] that the method is not based on random coding or maximal coding ideas, and it is this fact that makes it particularly suited for proving coding theorems for certain systems of channels with noiseless feedback.As a consequence of our results we obtain a formula for the zero-error capacity of a d.m.c.f., which was conjectured by Shannon ([8], p. 19). 相似文献
8.
《随机分析与应用》2013,31(4):935-951
Abstract In this paper, we investigate the stochastic stabilization problem for a class of linear discrete time‐delay systems with Markovian jump parameters. The jump parameters considered here is modeled by a discrete‐time Markov chain. Our attention is focused on the design of linear state feedback memoryless controller such that stochastic stability of the resulting closed‐loop system is guaranteed when the system under consideration is either with or without parameter uncertainties. Sufficient conditions are proposed to solve the above problems, which are in terms of a set of solutions of coupled matrix inequalities. 相似文献
9.
In this paper we consider the zero error variable length coding problem for discrete memoryless sources with side information at the decoder only. Using concepts of graph theory, we obtain a characterization of the minimum achievable rater for this coding problem. Furthermore, computable upper and lower bounds for the minimum achievable rater is given and a condition under which the upper and lower bounds are equal is found. Finally, this result is applied to some examples in which the minimum achievable rater can be evaluated. 相似文献
10.
Elizabeth Mansfield Gloria Marí Beffa Jing Ping Wang 《Foundations of Computational Mathematics》2013,13(4):545-582
Group-based moving frames have a wide range of applications, from the classical equivalence problems in differential geometry to more modern applications such as computer vision. Here we describe what we call a discrete group-based moving frame, which is essentially a sequence of moving frames with overlapping domains. We demonstrate a small set of generators of the algebra of invariants, which we call the discrete Maurer–Cartan invariants, for which there are recursion formulas. We show that this offers significant computational advantages over a single moving frame for our study of discrete integrable systems. We demonstrate that the discrete analogues of some curvature flows lead naturally to Hamiltonian pairs, which generate integrable differential-difference systems. In particular, we show that in the centro-affine plane and the projective space, the Hamiltonian pairs obtained can be transformed into the known Hamiltonian pairs for the Toda and modified Volterra lattices, respectively, under Miura transformations. We also show that a specified invariant map of polygons in the centro-affine plane can be transformed to the integrable discretization of the Toda Lattice. Moreover, we describe in detail the case of discrete flows in the homogeneous 2-sphere and we obtain realizations of equations of Volterra type as evolutions of polygons on the sphere. 相似文献
11.
Mowaffaq Hajja 《代数通讯》2013,41(11):4031-4041
Associated to a toric variety X of dimension r over a field k is a fan Δ on R1. The fan Δ is a finite set of cones which are in one-to-one correspondence with the orbits of the torus action on X. The fan Δ inherits the Zariski topology from X. In this article some cohomological invariants of X are studied in terms of whether or not they depend only on Δ and not k. Secondly some numerical invariants of X are studied in terms of whether or not they are topological invariants of the fan Δ. That is, whether or not they depend only on the finite topological space defined on Δ. The invariants with which we are mostly concerned are the class group of Weil divisors, the Picard group, the Brauer group and the dimensions of the torsion free part of the etale cohomology groups with coefficients in the sheaf of units. The notion of an open neighborhood of a fan is introduced and examples are given for which the above invariants are sufficiently fine to give nontrivial stratifications of an open neighborhood of a fan all of whose maximal cones are nonsimplicia. 相似文献
12.
Discrete autoregressive process of order 1 (DAR(1)) has been used as a popular stochastic model for correlated traffic sources because it parsimoniously uses a single parameter to capture the desirable correlation structure. In contrast with DAR(1), discrete autoregressive process of order 2 (DAR(2)) uses one more parameter to provide a much richer pattern in the autocorrelation function and is able to capture slower decay rate and longer memory. To investigate how the additional traffic parameter in DAR(2) influences the queueing performance, this paper provides an analysis of the discrete‐time DAR(2)/D/1 queue. The performance measures concerned are the mean and second‐order statistics of queue size, which are both important in the queueing systems seen in telecommunication networks. Under a mild condition, these performance indices are derived in closed form that allows for efficient computing. An approximate version of these results is also developed to relax the condition and cover more general sources, and both versions serve as a simple tool set for performance evaluation. The numerical examples use this tool to demonstrate that the DAR(2) source may cause up to 30% poorer performance than DAR(1) when the traffic is heavy, bursty, and highly correlated. This indicates that the effect from slower decay rate in autocorrelation is not negligible and using the extra parameter is necessary particularly when the queue is heavily loaded with correlated traffic. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
13.
The rank and invariants of a general lattice rule are conventionally defined in terms of the group-theoretic properties of the rule. Here we give a constructive definition of the rank and invariants using integer matrices. This underpins a nonabstract algorithm set in matrix algebra for obtaining the Sylow p-decomposition of a lattice rule. This approach is particularly useful when it is not known whether the form in which the lattice rule is specified is canonical or even repetitive. A new set of necessary and sufficient conditions for recognizing a canonical form is given. 相似文献
14.
Petra Bonfert-Taylor Edward C. Taylor 《Transactions of the American Mathematical Society》2003,355(2):787-811
We extend the part of Patterson-Sullivan theory to discrete quasiconformal groups that relates the exponent of convergence of the Poincaré series to the Hausdorff dimension of the limit set. In doing so we define new bi-Lipschitz invariants that localize both the exponent of convergence and the Hausdorff dimension. We find these invariants help to expose and explain the discrepancy between the conformal and quasiconformal setting of Patterson-Sullivan theory.
15.
The Frobenius automorphism of the function field allows to define some discrete birational invariants of algebraic manifolds
usingp
s
-th powers of differentials. Examples of algebraic hypersurfaces are sufficient to show the independence of the familiar birational
invariants. 相似文献
16.
The Frobenius automorphism of the function field allows to define some discrete birational invariants of algebraic manifolds
using p
s
-th powers of differentials. Examples of algebraic hypersurfaces are sufficient to show the independence of the familiar birational
invariants.
Received: Received: 6 March 1997 相似文献
17.
《Insurance: Mathematics and Economics》2009,44(3):368-376
Estimation of adequate reserves for outstanding claims is one of the main activities of actuaries in property/casualty insurance and a major topic in actuarial science. The need to estimate future claims has led to the development of many loss reserving techniques. There are two important problems that must be dealt with in the process of estimating reserves for outstanding claims: one is to determine an appropriate model for the claims process, and the other is to assess the degree of correlation among claim payments in different calendar and origin years. We approach both problems here. On the one hand we use a gamma distribution to model the claims process and, in addition, we allow the claims to be correlated. We follow a Bayesian approach for making inference with vague prior distributions. The methodology is illustrated with a real data set and compared with other standard methods. 相似文献
18.
Estimation of adequate reserves for outstanding claims is one of the main activities of actuaries in property/casualty insurance and a major topic in actuarial science. The need to estimate future claims has led to the development of many loss reserving techniques. There are two important problems that must be dealt with in the process of estimating reserves for outstanding claims: one is to determine an appropriate model for the claims process, and the other is to assess the degree of correlation among claim payments in different calendar and origin years. We approach both problems here. On the one hand we use a gamma distribution to model the claims process and, in addition, we allow the claims to be correlated. We follow a Bayesian approach for making inference with vague prior distributions. The methodology is illustrated with a real data set and compared with other standard methods. 相似文献
19.
In this paper, partially observable Markov decision processes (POMDPs) with discrete state and action space under the average reward criterion are considered from a recent-developed sensitivity point of view. By analyzing the average-reward performance difference formula, we propose a policy iteration algorithm with step sizes to obtain an optimal or local optimal memoryless policy. This algorithm improves the policy along the same direction as the policy iteration does and suitable step sizes guarantee the convergence of the algorithm. Moreover, the algorithm can be used in Markov decision processes (MDPs) with correlated actions. Two numerical examples are provided to illustrate the applicability of the algorithm. 相似文献
20.
James E Potter James C Deckert 《Journal of Mathematical Analysis and Applications》1973,43(2):293-320
In an earlier paper, the conservative and minimal bound to the crosscorrelation terms between estimation error and a random forcing function was presented. That bound was found to be a particular linear combination of the estimation error covariance and the forcing function covariance involving a free scalar parameter. The bound was then substituted for the cross-correlation terms in the differential equation for the estimation error covariance matrix in order to approximate its behavior between discrete measurement times. The time history of the free parameter which minimized a linear combination of the elements of the estimated covariance matrix at the next measurement time was found as the noniterative solution to an optimal control problem with a matrix state.In this paper, necessary and sufficient conditions are presented for the problem of minimizing a linear combination of the elements of the approximated estimation error covariance at the end of an interval in which are linearly incorporated a finite number of discrete vector measurements corrupted by white and/or correlated measurement noise. Although the determination of the optimal trajectory in general requires iteration, a particularly simple algorithm is presented. Numerical results are presented for the case of a satellite in a highly elliptic orbit about a model Earth. 相似文献