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1.
I. Vincze 《Journal of Mathematical Sciences》1997,84(3):1190-1196
After establishing the formula of information, we turn to two cases: to the independent case and to the dependent case. If
the characteristics of the particles (e.g., the energy) as random variables are independent, we come in the discrete case
to the Boltzmann distribution, while in the continuous case we come to the Gibbs formula-irrespectively of whether the particles
are distinguishable or not. Our effort is nimed at clarity of the ideas, not at their mathematical completeness.
Supported by the Hungarian National Foundation for Scientific Research (grant No. T 016384 and No. 4007-016237)
Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russian, 1995, Part III. 相似文献
2.
A. N. Chuprunov 《Lithuanian Mathematical Journal》1995,35(1):42-52
The paper deals with maxima and sums of independent random variables. These random variables are the values of independent
identically distributed stochastic processes at a random point in time. We obtain conditions for their weak convergence, at
almost all points in time to the same infinitely divisible distribution and describe the limit distribution for these sums.
Some applications of these results to statistics are considered.
This work was supported by the Russian Foundation for Fundamental Research (grant No. 93-011-16099).
Research Institute of Mathematics and Mechanics, Kazan State University, 17 Universitetskaya St., Kazan, 420008, Russia. Translated
from Lietuvos Matematikos Rinkinys, Vol. 5, No. 1, pp. 52–64, January–March, 1995.
Translated by A. N. Chuprunov 相似文献
3.
A. N. Chuprunov 《Journal of Mathematical Sciences》1996,78(1):34-47
The paper deals with random variables which are the values of independent identically distributed stochastic processes at
random points in time. We obtain conditions for the weak convergence of their sums, at almost all points in time, to the same
infinitely divisible distribution and describe the limit distribution for these sums. Also we obtain an analog of the Donsker
theorem and limit theorems for empirical processes for such random variables.
Supported by the Russian Foundation for Fundamental Research (grant No. 93-011-16099).
Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part II, Eger, Hungary, 1994. 相似文献
4.
In this paper, based on theorems for limit distributions of empirical power processes for the i.i.d. case and for the case
with independent triangular arrays of random variables, we prove limit theorems for U- and V-statistics determined by generalized
polynomial kernel functions. We also show that under some natural conditions the limit distributions can be represented as
functionals on the limit process of the normed empirical power process. We consider the one-sample case, as well as multi-sample
cases.
Dedicated to Professor V. M. Zolotarev on his sixty-fifth birthday.
Supported by the Hungarian National Foundation for Scientific Research (grant No. T1666).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I. 相似文献
5.
O. I. Klesov 《Journal of Mathematical Sciences》1995,76(2):2241-2249
The complete convergence of normed sums of independent identically distributed random variables with random indices is studied.
Some applications for subsequences and sequences with multidimensional indices are given.
Supported by the Hungarian Foundation for Scientific Research (grant OTKA-1650/1991).
Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part I, Eger, Hungary, 1994. 相似文献
6.
In terms of the mean metric, a convergence rate estimate is obtained in a limit theorem for random symmetric polynomials.
Supported by the Russian Foundation for Fundamental Research (grant No. 96-01-01920) and by the Hungarian National Foundation
for Scientific Research (grant No. T 16665).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part 11. 相似文献
7.
A. N. Chuprunov 《Journal of Mathematical Sciences》1995,76(1):2110-2117
The paper deals with sums of independent and identically distributed random variables defined on some probability space which
are multiplied by random coefficients. These coefficients are the values of independent random variables defined on another
probability space. We obtain conditions for the weak convergence of weighted sums, for almost all coefficients, to some infinitely
divisible distribution. The limit distribution for these sums is found.
Supported by the Russian Foundation for Fundamental Research (grant No. 93-011-16099).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, 1993. 相似文献
8.
V. Yu. Korolev 《Journal of Mathematical Sciences》1995,76(1):2153-2162
Under different assumptions, necessary and sufficient conditions are given for the weak convergence of sums of a random number
of independent identically distributed random variables.
Supported by the Russian Foundation for Fundamental Researches (grant No. 93-011-1446).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, 1993. 相似文献
9.
Necessary and sufficient conditions are presented for the weak convergence of random sums of independent identically distributed
random variables in the double array scheme. As corollaries, two criteria of the normal convergence of random sums are given.
Supported by the Russian Foundation for Fundamental Research (grant No. 96-011-01919).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I. 相似文献
10.
J. Sztrik 《Journal of Mathematical Sciences》2000,99(4):1476-1484
This paper deals with a first-come, first-served (FCFS) queueing model to analyze the asymptotic behavior of a heterogeneous
finite-source communication system with a single processor. Each source and the processor are assumed to operate in independent
random environments, allowing the arrival and service processes to be Markov-modulated ones. Each message is characterized
by its own exponentially distributed source and processing time with parameter, depending on the state of the corresponding
environment, that is, the arrival and service rates are subject to random fluctuations. Assuming that the arrival rates of
the messages are many times greater than their service rates (“fast” arrival), it is shown that the time to the first system
failure converges in distribution, under appropriate norming, to an exponentially distributed random variable. Some simple
examples are considered to illustrate the effectiveness of the method proposed by comparing the approximate results to the
exact ones.
Supported by the Hungarian National Foundation for Scientific Research (grant No. OTKA T14974/95).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part II. 相似文献
11.
V. M. Kruglov 《Journal of Mathematical Sciences》1998,91(3):2942-2948
The law of large numbers for weighted sums of independent identically distributed random variables due to Chow and Lai is
generalized to nonidentically distributed or pairwise independent summands.
Supported by the Russian Foundation for Fundamental Research (grant No. 96-01-01920).
Proceedings of the Seminar on Stability Problems for Stochastic, Models, Moscow, Russia, 1996, Part. II. 相似文献
12.
Necessary and sufficient conditions are presented for sums of asymptotically independent random variables to converge to a
normal random variable in the sense of total variation distance, uniform metric for characteristic functions. and mean metric
of order q.
Supported by the Russian Foundation for Fundamental Research (grant No. 96-01-01920).
Proceedings of the Seminar on Stability Problems for Stochastic Models. Moscow. Russia. 1996. Part II. 相似文献
13.
Nonlinear functional errors-in-variables models with error terms satisfying mixing conditions are studied. It is pointed out
that under certain conditions the least-squares estimator of regression parameters is not consistent. An alternative estimator
for regression parameters is proposed. The consistency of the alternative estimator is established.
Supported by the Hungarian Foundation for Scientific Research (grant No. OTKA-T19501-1996) and by the Hungarian Ministry of
Culture and Education (grant No. 179-1995).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part I. 相似文献
14.
In this paper, we consider a stochastic queueing model for the performance evaluaton of a real-life computer system consisting
of n terminals connected with a CPU. A user at terminal i has thinking and processing time depending on the index i. Let us
suppose that the operational system is subject to random breakdowns, which may be software or hardware ones, stopping the
service both at the terminals and at the CPU. The failure-free operation times of the system and the restoration times are
random variables. Busy terminals are also subject to random breakdowns not affecting the system operation. The failure-free
operation times and the repair times of a busy terminal i are random variables with distribution function depending on index
i. The breakdowns are serviced by a single repairman providing preemptive priority to the system's failure, while the restoration
at the terminals are carried out according to the FIFO rule. We assume that each user generates only one job at a time, and
he waits at the CPU before he starts thinking again, that is, the terminal is inactive while waiting at the CPU, and it cannot
break down. All random variables involved in the model construction are assumed to be exponentially distributed and independent
of each other. The aim of this paper is to investigate the effect of different service disciplines, such as FIFO, processor
sharing, priority processor sharing, and polling, on the main performance measures, such as utilizations, response times,
throughput, and mean queue length.
Supported by the Hungarian National Foundation for Scientific Research (grant No. ORKA T014974/95).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló. Hungary, 1997, Part II. 相似文献
15.
H. Andréka 《Algebra Universalis》1991,28(2):274-279
We prove that relation algebras cannot be denned with one variable over the class of semi-associative relation algebras, while it can be defined with equations using two variables, over the class of all Boolean algebras.Presented by Jan Mycieiski.Research supported by Hungarian National Foundation for Scientific Research grant No. 1810. 相似文献
16.
The paper present necessary and sufficient conditions for the weak convergence of Rm-valued random sequences with independent random indices under some additional assumptions. Operator normalization is considered.
Supported by the Russian Foundation for Fundamental Research (grant No. 93-01-01446).
Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part I, Eger, Hungary, 1994. 相似文献
17.
We establish particular wavelet-based decompositions of Gaussian stationary processes in continuous time. These decompositions
have a multiscale structure, independent Gaussian random variables in high-frequency terms, and the random coefficients of
low-frequency terms approximating the Gaussian stationary process itself. They can also be viewed as extensions of the earlier
wavelet-based decompositions of Zhang and Walter (IEEE Trans. Signal Process. 42(7):1737–1745, [1994]) for stationary processes, and Meyer et al. (J. Fourier Anal. Appl. 5(5):465–494, [1999]) for fractional Brownian motion. Several examples of Gaussian random processes are considered such as the processes with
rational spectral densities. An application to simulation is presented where an associated Fast Wavelet Transform-like algorithm
plays a key role.
The second author was supported in part by the NSF grant DMS-0505628. 相似文献
18.
Janos Karatson 《Applications of Mathematics》2005,50(3):277-290
A mesh independent bound is given for the superlinear convergence of the CGM for preconditioned self-adjoint linear elliptic problems using suitable equivalent operators. The results rely on K-condition numbers and related estimates for compact Hilbert-Schmidt operators in Hilbert space.This research was supported by the Hungarian National Research Fund OTKA under grant No. T043765. 相似文献
19.
This paper deals with a nonhomogeneous finite-source queueing model to describe the performance of a multiterminal system
subject to random breakdowns under the polling service discipline. The model studied here is a closed queueing network which
has three service stations. a CPU (single server), terminals (infinite server), a repairman (single server), and a finite
number of customers (jobs) that have distinct service rates at the service stations. The CPU's repair has preemptive priority
over the terminal repairs, and failure of the CPU stops the service of the other stations, thus the nodes are not independent.
It can be viewed as a continuation of papers by the authors (see references), which discussed a FIFO (first-in, first-out)
and a PPS (priority processor sharing) serviced queueing model subject to random breakdowns. All random variables are assumed
to be independent and exponentially distributed. The system behavior can be described by a Markov chain, but the number of
states is very large. The purpose of this paper is to give a recursive computational approach to solve steady-state equations
and to illustrate the problem in question using some numerical results.
Supported by the Hungarian National Foundation for Scientific Research (grant Nos. OTKA T014974/95 and T016933/95)
Proceedings of the Seminar on Stability Problems for Stochastic Models. Hajdúszoboszló, Hungary, 1997, Part, II. 相似文献
20.
J. Fritz 《Probability Theory and Related Fields》1989,81(2):291-318
Summary A lattice system of interacting diffusion processes is investigated. The evolution is attractive and time reversible, the spin satisfies a conservation law. It is shown that the rescaled spin field converges in probability to the corresponding solution to a nonlinear diffusion equation.Supported in part by the Hungarian National Foundation for Scientific Research, grant No. 819/1, and by the Mathematical Department of Rutgers University, N.S.F. grant DMR 8612369 相似文献