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1.
For a Poisson process with exponentially distributed negative component, we obtain integral transforms of the joint distribution
of the time of the first exit from an interval and the value of the jump over the boundary at exit time and the joint distribution
of the time of the first hit of the interval and the value of the process at this time. On the exponentially distributed time
interval, we obtain distributions of the total sojourn time of the process in the interval, the joint distribution of the
supremum, infimum, and value of the process, the joint distribution of the number of upward and downward crossings of the
interval, and generators of the joint distribution of the number of hits of the interval and the number of jumps over the
interval.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 7, pp. 922–953, July, 2006. 相似文献
2.
Several two-boundary problems are solved for a special Lévy process: the Poisson process with an exponential component. The
jumps of this process are controlled by a homogeneous Poisson process, the positive jump size distribution is arbitrary, while
the distribution of the negative jumps is exponential. Closed form expressions are obtained for the integral transforms of
the joint distribution of the first exit time from an interval and the value of the overshoot through boundaries at the first
exit time. Also the joint distribution of the first entry time into the interval and the value of the process at this time
instant are determined in terms of integral transforms. 相似文献
3.
We solve main two-boundary problems for a random walk. The generating function of the joint distribution of the first exit
time of a random walk from an interval and the value of the overshoot of the random walk over the boundary at exit time is
determined. We also determine the generating function of the joint distribution of the first entrance time of a random walk
to an interval and the value of the random walk at this time. The distributions of the supremum, infimum, and value of a random
walk and the number of upward and downward crossings of an interval by a random walk are determined on a geometrically distributed
time interval. We give examples of application of obtained results to a random walk with one-sided exponentially distributed
jumps.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 11, pp. 1485–1509, November, 2007. 相似文献
4.
We study a BMAP/>SM/1 queue with batch Markov arrival process input and semi‐Markov service. Service times may depend on arrival
phase states, that is, there are many types of arrivals which have different service time distributions. The service process
is a heterogeneous Markov renewal process, and so our model necessarily includes known models. At first, we consider the first
passage time from level {κ+1} (the set of the states that the number of customers in the system is κ+1) to level {κ} when a batch arrival occurs at time 0 and then a customer service included in that batch simultaneously starts. The service
descipline is considered as a LIFO (Last‐In First‐Out) with preemption. This discipline has the fundamental role for the analysis
of the first passage time. Using this first passage time distribution, the busy period length distribution can be obtained.
The busy period remains unaltered in any service disciplines if they are work‐conserving. Next, we analyze the stationary
workload distribution (the stationary virtual waiting time distribution). The workload as well as the busy period remain unaltered
in any service disciplines if they are work‐conserving. Based on this fact, we derive the Laplace–Stieltjes transform for
the stationary distribution of the actual waiting time under a FIFO discipline. In addition, we refer to the Laplace–Stieltjes
transforms for the distributions of the actual waiting times of the individual types of customers. Using the relationship
between the stationary waiting time distribution and the stationary distribution of the number of customers in the system
at departure epochs, we derive the generating function for the stationary joint distribution of the numbers of different types
of customers at departures.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
We study correlation functions of the totally asymmetric simple exclusion process (TASEP) in discrete time with backward sequential
update. We prove a determinant formula for the generalized Green’s function describing transitions between particle positions
at given instants. As an example, we calculate the current correlation function, i.e., the joint probability distribution
of times required by each particle to travel a given distance. An asymptotic analysis shows that current fluctuations converge
to the Airy
2
process. 相似文献
6.
Let {Z
t
,t≥1} be a sequence of trials taking values in a given setA={0, 1, 2,...,m}, where we regard the value 0 as failure and the remainingm values as successes. Let ε be a (single or compound) pattern. In this paper, we provide a unified approach for the study
of two joint distributions, i.e., the joint distribution of the numberX
n
of occurrences of ε, the numbers of successes and failures inn trials and the joint distribution of the waiting timeT
r
until ther-th occurrence of ε, the numbers of successes and failures appeared at that time. We also investigate some distributions as
by-products of the two joint distributions. Our methodology is based on two types of the random variablesX
n
(a Markov chain imbeddable variable of binomial type and a Markov chain imbeddable variable of returnable type). The present
work develops several variations of the Markov chain imbedding method and enables us to deal with the variety of applications
in different fields. Finally, we discuss several practical examples of our results.
This research was partially supported by the ISM Cooperative Research Program (2002-ISM·CRP-2007). 相似文献
7.
P. A. Scarf 《商业与工业应用随机模型》1993,9(3):267-278
The connection between extreme values and record-low values is exploited to derive simply the limiting joint distribution of the r largest order statistics. The use of this distribution in the modelling of corrosion phenomena is considered, and the extrapolation of maxima in space and time is described in this context. There has been recent emphasis on movement away from classical extreme value theory to more efficient estimation procedures. This shift is continued with the illustration of the extra precision of predicted maxima obtained from a model based on extreme order statistics over the classical extreme value approach. 相似文献
8.
Firstly, we compute the distribution function for the hitting time of a linear time-dependent boundary t ↦ a + bt, a ≥ 0, b ∈ ℝ, by a reflecting Brownian motion. The main tool hereby is Doob’s formula which gives the probability that Brownian motion
started inside a wedge does not hit this wedge. Other key ingredients are the time inversion property of Brownian motion and
the time reversal property of diffusion bridges. Secondly, this methodology can also be applied for the three-dimensional
Bessel process. Thirdly, we consider Bessel bridges from 0 to 0 with dimension parameter δ > 0 and show that the probability that such a Bessel bridge crosses an affine boundary is equal to the probability that this
Bessel bridge stays below some fixed value. 相似文献
9.
We consider a closed queueing network, consisting of two FCFS single server queues in series: a queue with general service times and a queue with exponential service times. A fixed number \(N\) of customers cycle through this network. We determine the joint sojourn time distribution of a tagged customer in, first, the general queue and, then, the exponential queue. Subsequently, we indicate how the approach toward this closed system also allows us to study the joint sojourn time distribution of a tagged customer in the equivalent open two-queue system, consisting of FCFS single server queues with general and exponential service times, respectively, in the case that the input process to the first queue is a Poisson process. 相似文献
10.
N. G. Dokuchaev 《Journal of Mathematical Sciences》2000,99(2):1075-1088
We deduce equations for the probability distribution of a value similar to the local occupation time of a diffusion process
on a hypersurface. A stochastic control problem for the local occupation time is considered. Bibliography: 13 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 244, 1997, pp. 96–118.
Translated by S. Yu. Pilyugin. 相似文献
11.
Konstantin Avrachenkov Patrick Brown Natalia Osipova 《Annals of Operations Research》2009,170(1):21-39
We analyze the Two Level Processor Sharing (TLPS) scheduling discipline with the hyper-exponential job size distribution and
with the Poisson arrival process. TLPS is a convenient model to study the benefit of the file size based differentiation in
TCP/IP networks. In the case of the hyper-exponential job size distribution with two phases, we find a closed form analytic
expression for the expected sojourn time and an approximation for the optimal value of the threshold that minimizes the expected
sojourn time. In the case of the hyper-exponential job size distribution with more than two phases, we derive a tight upper
bound for the expected sojourn time conditioned on the job size. We show that when the variance of the job size distribution
increases, the gain in system performance increases and the sensitivity to the choice of the threshold near its optimal value
decreases.
The work was supported by France Telecom R&D Grant “Modélisation et Gestion du Trafic Réseaux Internet” no. 46129414. 相似文献
12.
In this paper we solve a two-sided exit problem for a difference of a compound Poisson process and a compound renewal process. More specifically, we determine the Laplace transforms of the joint distribution of the first exit time, the value of the overshoot and the value of a linear component at this time instant. The results obtained are applied to solve the two-sided exit problem for a particular class of stochastic processes, i.e. the difference of the compound Poisson process and the renewal process whose jumps are exponentially distributed. The advantage is that these results are in a closed form, in terms of resolvent sequences of the process. We determine the Laplace transforms of the busy period of the systems M ? |G δ |1|B, G δ |M ? |1|B in case when δ~exp?(λ). Additionally, we prove the weak convergence of the two-boundary characteristics of the process to the corresponding functionals of the standard Wiener process. 相似文献
13.
A limit theorem with bounds on the rate of convergence is proven. The joint distribution of a fixed number of relative decrements
of the top order statistics from a random sample converges to the limit as the sample size increases if and only if the underlying
distribution is in essence a Pareto. In conjunction with a chi-square test of fit, it provides an asymptotically distribution-free
test of fit to the family of distributions with regularly varying tails at infinity. When the limit distribution holds, rank-size
plots obey Zipf’s law. The test can be used to detect departures from this Zipf–Pareto law.
相似文献
14.
应用逐段决定马尔可夫过程理论及补充变量技巧,使Markov-modulated风险过程成为齐次强马尔可夫过程,然后利用强马氏性及首达时间分布给出了其破产前最大盈余额与破产赤字的联合分布. 相似文献
15.
This paper considers stationary queues with multiple arrival streams governed by an irreducible Markov chain. In a very general setting, we first show an invariance relationship between the time-average joint queue length distribution and the customer-average joint queue length distribution at departures. Based on this invariance relationship, we provide a distributional form of Little's law for FIFO queues with simple arrivals (i.e., the superposed arrival process has the orderliness property). Note that this law relates the time-average joint queue length distribution with the stationary sojourn time distributions of customers from respective arrival streams. As an application of the law, we consider two variants of FIFO queues with vacations, where the service time distribution of customers from each arrival stream is assumed to be general and service time distributions of customers may be different for different arrival streams. For each queue, the stationary waiting time distribution of customers from each arrival stream is first examined, and then applying the Little's law, we obtain an equation which the probability generating function of the joint queue length distribution satisfies. Further, based on this equation, we provide a way to construct a numerically feasible recursion to compute the joint queue length distribution. 相似文献
16.
Yuri Kifer 《Israel Journal of Mathematics》1981,40(1):74-96
We consider the Markov diffusion process ξ∈(t), transforming when ɛ=0 into the solution of an ordinary differential equation with a turning point ℴ of the hyperbolic type.
The asymptotic behevior as ɛ→0 of the exit time, of its expectation of the probability distribution of exit points for the
process ξ∈(t) is studied. These indicate also the asymptotic behavior of solutions of the corresponding singularly perturbed elliptic
boundary value problems. 相似文献
17.
18.
We study the continuous time integer valued process , which jumps to each of its two nearest neighbors at the rate of one plus the total time the process has previously spent
at that neighbor. We show that the proportion of the time before t which this process spends at integers j converges to positive random variables V
j
, which sum to one, and whose joint distribution is explicitly described. We also show
Received: 19 December 2000 / Revised version: 1 November 2001 / Published online: 17 May 2002 相似文献
19.
A. Laurinčikas 《Lithuanian Mathematical Journal》1999,39(1):51-57
The joint limit distribution of functions given by Dirichlet series is studied. The necessary and sufficient condition when
this distribution is a product of marginal distributions is found. An example of such Dirichlet series with linear independent
systems of exponents is presented.
Partially supported by the Lithuanian State Science and Studies Foundation.
Vilnius University, Naugarduko 24, 2006 Vilnius; Šiauliai University, P. Višinskio 25, 5419 Šiauliai, Lithuania. Translated
from Lietuvos Matematikos Rinkinys, Vol. 39, No. 1, pp. 65–73, January–March, 1999.
Translated by A. Laurinčikas 相似文献
20.
On the basis of a given sequence of independent identically distributed pairs of random variables, we construct the step process
of semi-Markov random walk that is later delayed by a screen at zero. For this process, we obtain the Laplace transform of
the distribution of the time of the first hit of the level zero.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 7, pp. 912–919, July, 2007. 相似文献