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1.
In this paper, by exploiting recent results on the pathwise behavior of the workload process in single server, work conserving queues of theG/G/1/ type, we show that the workload of multiserver, work conserving queues ofG/G/m/ (m<) (andG/G/) queues satisfies an o(t) growth condition, provided that the time average of the work brought into the system is less thanm form < (and finite form=).  相似文献   

2.
Summary LetL(F ) be theII 1-factor defined by the free groupF in infinite number of generators. It is shown that for a class of automorphisms ofL(F ) arising from bijections of the set of generators ofF on itself, and including the free shift, the entropy is zero.Oblatum 15-III-1992  相似文献   

3.
Summary Consider a random walk of law on a locally compact second countable groupG. Let the starting measure be equivalent to the Haar measure and denote byQ the corresponding Markov measure on the space of pathsG . We study the relation between the spacesL (G , a ,Q) andL (G , i ,Q) where a and i stand for the asymptotic and invariant -algebras, respectively. We obtain a factorizationL (G , a ,Q) L (G , i ,Q)L (C) whereC is a cyclic group whose order (finite or infinite) coincides with the period of the Markov shift and is determined by the asymptotic behaviour of the convolution powers n.  相似文献   

4.
We consider a functional differential equation (1) (t)=F(t,) fort[0,+) together with a generalized Nicoletti condition (2)H()=. The functionF: [0,+)×C 0[0,+)B is given (whereB denotes the Banach space) and the value ofF (t, ) may depend on the values of (t) fort[0,+);H: C 0[0,+)B is a given linear operator and B. Under suitable assumptions we show that when the solution :[0,+)B satisfies a certain growth condition, then there exists exactly one solution of the problem (1), (2).  相似文献   

5.
Summary A general theory of stochastic integral in the abstract topological measurable space is established. The martingale measure is defined as a random set function having some martingale property. All square integrable martingale measures constitute a Hilbert space M 2. For each M 2, a real valued measure on the predictable -algebra is constructed. The stochastic integral of a random function with respect to is defined and investigated by means of Riesz's theorem and the theory of projections. The stochastic integral operator I is an isometry from L 2() to a stable subspace of M 2, its inverse is defined as a random Radon-Nikodym derivative. Some basic formulas in stochastic calculus are obtained. The results are extended to the cases of local martingale and semimartingale measures as well.  相似文献   

6.
In this paper we consider the equation y +q(t)y + p(t)h(y)=0, where p, q are real valued continuous functions on [0, ) such that q(t) 0, p(t) 0 and h(y) is continuous in (–, ) such that h(y)y > 0 for y 0. We obtain sufficient conditions for solutions of the considered equation to be nonoscillatory. Furthermore, the asymptotic behaviour of these nonoscillatory solutions is studied.  相似文献   

7.
It is proved that for any sequence {R k} k=1 of real numbers satisfyingR kk (k1) andR k=o(k log2 k),k, there exists an orthonormal system {n k(x)} n=1 ,x (0;1), such that none of its subsystems {n k(x)} k=1 withn kRk (k1) is a convergence subsystem.  相似文献   

8.
Let {n} be a sequence of identically distributed independent random variables,M1=<0,M 1 2 <;S 0=0,S n =1+2,+...+ n, n1;¯ S=sup {S n n=0.} The asymptotic behavior ofP(¯ St) as t is studied. If t P (1x dx=0((t)), thenP(¯ St)– 1/¦¦ t P (1x dx=0((t)) (t) is a positive function, having regular behavior at infinity.Translated from Matematicheskie Zametki, Vol. 22, No. 5, pp. 763–770, November, 1977.The author thanks B. A. Rogozin for the formulation of the problem and valuable remarks.  相似文献   

9.
Summary In this paper, the object of study is reflected Brownian motion in a cone ind-dimensions (d3) with nonconstant oblique reflection on each radial line emanating from the vertex of the cone. The basic question considered here is When is this process a semimartingale?. Conditions for the existence and uniqueness of the process for which the vertex is an instantaneous state were given by Kwon, which is resolved in terms of a real parameter depending on the cone and the direction of reflection. It is shown that starting from any point of the cone, the process is a semimartingale if < 1, + 0 and not a semimartingale if < < 2.This research is supported by KOSEF grant 941-0100-011-1  相似文献   

10.
Consider a triangular array of standard Gaussian random variables {n,i, i 0, n 1} such that {n,i, i 0} is a stationary normal sequence for each n 1. Let n,k = corr(n,i,n,i+k). If (1-n,k)log n k (0,) as n for some k, then the locations where the extreme values occur cluster and the limiting distribution of the maxima is still the Gumbel distribution as in the stationary or i.i.d. case, but shifted by a parameter measuring the clustering. Triangular arrays of Gaussian sequences are used to approximate a continuous Gaussian process X(t), t 0. The cluster behavior of the random sequence refers to the behavior of the extremes values of the continuous process. The relation is analyzed. It reveals a new definition of the constants H used for the limiting distribution of maxima of continuous Gaussian processes and provides further understanding of the limit result for these extremes.  相似文献   

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