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Communications in Statistics. Stochastic Models最新文献

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A novel computational method for solving finite qbd processes 求解有限qbd过程的一种新的计算方法
Communications in Statistics. Stochastic Models Pub Date : 2000-01-01 DOI: 10.1080/15326340008807588
N. Akar, N. C. Oguz, K. Sohraby
{"title":"A novel computational method for solving finite qbd processes","authors":"N. Akar, N. C. Oguz, K. Sohraby","doi":"10.1080/15326340008807588","DOIUrl":"https://doi.org/10.1080/15326340008807588","url":null,"abstract":"We present a novel numerical method that exploits invariant subspace computations for finding the stationary probability distribution of a finite QBD process. Assuming that the QBD state space is defined in two dimensions with m phases and K+1 levels, the solution vector π k for level , is known to be expressible in the mixed matrix-geometric form , where R 1and R 2are certain solutions to two quadratic matrix equations, and v 1and v 2are vectors to be determined using the boundary conditions. We show that the matrix-geometric factors R 1and R 2can be simultaneously obtained irrespective of K via finding arbitrary bases for the left-and right-invariant subspaces of a certain real matrix of size 2m To find these bases, we employ either Schur decomposition or a matrix-sign function iteration with quadratic convergence rate. The vectors v 1and v 2are obtained by solving a linear matrix equation, which is constructed with a time complexity of . Therefore, the effect of the number of levels on the overall complexity is minimal. Besides its numerical efficiency, the proposed method is numerically stable, and in the limiting case of , it is shown to yield the well-known matrix-geometric solution for infinite QBD processes. We also extend the method to the cases of level-dependent and non-canonical transitions, and provide a numerical example to demonstrate its computational features in comparison with other well-known methods","PeriodicalId":341912,"journal":{"name":"Communications in Statistics. Stochastic Models","volume":"185 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116145076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 31
Inventory management at service facilities for systems with arbitrarily distributed service times 服务时间任意分布的系统的服务设施的库存管理
Communications in Statistics. Stochastic Models Pub Date : 2000-01-01 DOI: 10.1080/15326340008807592
O. Berman, K. Sapna
{"title":"Inventory management at service facilities for systems with arbitrarily distributed service times","authors":"O. Berman, K. Sapna","doi":"10.1080/15326340008807592","DOIUrl":"https://doi.org/10.1080/15326340008807592","url":null,"abstract":"This article analyzes an inventory system for service facilities where there is limited waiting space for customers. For service facilities, typically inventory is used during the provision of service. We consider a system with Poisson arrivals, arbitrarily distributed service times and zero leadtimes. Optimal value of the maximum allowable inventory that minimizes the long-run expected cost rate is obtained in an elegant manner. Various examples of service distributions and optimal values for maximum inventory in each of these cases is also presented. Our analysis also yields a closed form expression of the stationary distribution for the embedded Markov chain of an M/G/l finite capacity queue","PeriodicalId":341912,"journal":{"name":"Communications in Statistics. Stochastic Models","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121584129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 110
Quasistationary distributions for level-dependent quasi-birth-and-death processes 水平相关的准生与死过程的准平稳分布
Communications in Statistics. Stochastic Models Pub Date : 2000-01-01 DOI: 10.1080/15326340008807602
N. G. Bean, P. Pollett, P. Taylor
{"title":"Quasistationary distributions for level-dependent quasi-birth-and-death processes","authors":"N. G. Bean, P. Pollett, P. Taylor","doi":"10.1080/15326340008807602","DOIUrl":"https://doi.org/10.1080/15326340008807602","url":null,"abstract":"In this paper we provide a complete quasistationary analysis for the class of level-dependent, discrete-time quasi-birth-and-death processes (QBDs) for which level zero has been collapsed into an absorbing state. We show that the form of a quasistationary distribution depends upon whether the eigenvalue of a certain matrix is equal to one or less than one. Furthermore, we show how to calculate the convergence norm a of such a QBD and observe that the QBD is a-recurrent in the first case mentioned above and a-transient in the second case. The further classification of an a-recurrent QBD as a-positive or a-null depends on whether the convergence radius a2 of the modified QBD in which level one is collapsed into an absorbing state is strictly greater than, or equal to, a. In the first of these cases the QBD is a-positive, while in the second case the QBD may be a-positive or a-null","PeriodicalId":341912,"journal":{"name":"Communications in Statistics. Stochastic Models","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124778419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 20
Maximum-entropy distributions of nonnegative random variables with conditional-additive structure 条件加性结构非负随机变量的最大熵分布
Communications in Statistics. Stochastic Models Pub Date : 2000-01-01 DOI: 10.1080/15326340008807599
A. Dukhovny
{"title":"Maximum-entropy distributions of nonnegative random variables with conditional-additive structure","authors":"A. Dukhovny","doi":"10.1080/15326340008807599","DOIUrl":"https://doi.org/10.1080/15326340008807599","url":null,"abstract":"The principle of maximum entropy (ME) is used to obtain distributions of a nonnegative random variable X with conditional-additive structure: for each value of a finite control factor ηX is a sum of components whose conditional expectations (given the value of η) are known. We show that the ME distribution of X is a convex combination of convolutions of geometric sequences or exponential distributions for integer or continuous X, respectively, and find the distribution of η. In the integer case, we apply the method of “matrix unfolding” to the probability generating function of X and show that the probabilities can be blocked in rows that form a general matrix-geometric sequence. Studying an M/G/ l queueing system where the service time has conditional-additive structure, we show that the stationary queue-length probabilities can be blocked in a general matrix-geometric sequence of rows and evaluated by simple real-arithmetic matrix computations","PeriodicalId":341912,"journal":{"name":"Communications in Statistics. Stochastic Models","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133236997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
European option pricing when the riskfree interest rate follows a jump process 无风险利率时的欧式期权定价遵循一个跳跃过程
Communications in Statistics. Stochastic Models Pub Date : 2000-01-01 DOI: 10.1080/15326340008807580
A. Tsoi, Hailiang Yang, Shu-Ngai Yeung
{"title":"European option pricing when the riskfree interest rate follows a jump process","authors":"A. Tsoi, Hailiang Yang, Shu-Ngai Yeung","doi":"10.1080/15326340008807580","DOIUrl":"https://doi.org/10.1080/15326340008807580","url":null,"abstract":"In this paper, we analyze the pricing of European option when the riskfree interest rate follows a jump process. An expression for European call price is first obtained in the case of constant volatility. Then we present a general formulation which takes care of the variation of volatility. In this general formulation we utilize a point process filtering technique to estimate the state process. Finally we carry out some numerical simulation of our results","PeriodicalId":341912,"journal":{"name":"Communications in Statistics. Stochastic Models","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129758881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Gussian diffusions and continuous state branching processes with killing 高斯扩散和带杀伤的连续状态分支过程
Communications in Statistics. Stochastic Models Pub Date : 2000-01-01 DOI: 10.1080/15326340008807584
H. Frydman
{"title":"Gussian diffusions and continuous state branching processes with killing","authors":"H. Frydman","doi":"10.1080/15326340008807584","DOIUrl":"https://doi.org/10.1080/15326340008807584","url":null,"abstract":"This work considers a diffusion process , subject to killing at a rate which depends on time and current value of a diffusion. A conditioned process is defined, on , by restricting the sample space of , to the sample paths which survived up to time t. It is shown that conditioned process is a diffusion whose infinitesimal parameters are functions of the infinitesimal parameters of , and of the survival function of . This result is applied to the problem of identification of a parametric form of a killing-rate function such that an unconditioned and an associated conditioned diffusion belong to the same family of diffusions. The specific results are obtained for Gaussian diffusions and for continuous state branching processes. For these diffusions the required killing-rate functions are identified and the properties of associated diffusions are discussed. In particular formulas for marginal survival functions of these diffusions are obtained. A general formula for the survival function of a diffusion when the values of a diffusion are known at discrete times is also discussed. The applications of this work to survival analysis and possible extensions are indicated","PeriodicalId":341912,"journal":{"name":"Communications in Statistics. Stochastic Models","volume":"196 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127596731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Occupation times in markov processes 马尔可夫过程中的占用时间
Communications in Statistics. Stochastic Models Pub Date : 2000-01-01 DOI: 10.1080/15326340008807601
B. Sericola
{"title":"Occupation times in markov processes","authors":"B. Sericola","doi":"10.1080/15326340008807601","DOIUrl":"https://doi.org/10.1080/15326340008807601","url":null,"abstract":"In a homogeneous finite-state Markov process, we consider the occupation times, that is, the times spent by the process in given subsets of the state space during a finite interval of time. We first derive the distribution of the occupation time of one subset and then we generalize that result to the joint distribution of occupation times of different subsets of the state space by the use of order statistics from the uniform distribution. Next, we consider the distribution of weighted sums of occupation times. We obtain forward and backward equations describing the behavior of these weighted sums and we show how these lead to simple expressions for that distribution","PeriodicalId":341912,"journal":{"name":"Communications in Statistics. Stochastic Models","volume":"301 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132707325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 65
Stochastic block–monotonicity in the approximation of the stationary distribution of infinite markov chains 无限马尔可夫链平稳分布近似中的随机块单调性
Communications in Statistics. Stochastic Models Pub Date : 2000-01-01 DOI: 10.1080/15326340008807589
Haijun Li, Yiqiang Q. Zhao
{"title":"Stochastic block–monotonicity in the approximation of the stationary distribution of infinite markov chains","authors":"Haijun Li, Yiqiang Q. Zhao","doi":"10.1080/15326340008807589","DOIUrl":"https://doi.org/10.1080/15326340008807589","url":null,"abstract":"Markov chains with block-structured transition matrices find many applications in various areas. Such Markov chains are characterized by having a state space which is partitioned into levels, each level consisting of a number of stages. Examples include Markov chains of GI/M/1 type and M/G/l type, and, more generally, Markov chains of Toeplitz type. The level-dependent quasi-birth-and-death (LDQBD) process provides an additional example; the transition matrix does not have repeating blocks in this case. In the analysis of such Markov chains, a number of properties and/or measures which relate to transitions among levels play a dominant role, while transitions between stages within the same level are less important In this paper, we introduce the concept of block-monotonicity and apply this notion to the analysis of Markov chains possessing block structure. In particular, the problem of approximating the stationary probability vectors is successfully treated","PeriodicalId":341912,"journal":{"name":"Communications in Statistics. Stochastic Models","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128941912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 22
A branching process model of telomere shortening 端粒缩短的分支过程模型
Communications in Statistics. Stochastic Models Pub Date : 2000-01-01 DOI: 10.1080/15326340008807581
P. Olofsson
{"title":"A branching process model of telomere shortening","authors":"P. Olofsson","doi":"10.1080/15326340008807581","DOIUrl":"https://doi.org/10.1080/15326340008807581","url":null,"abstract":"A branching process model of a certain cell population is considered. The population is divided into types according to the number of remaining chromosome end units. This leads to a reducible multi-type Bellman-Harris branching process which turns out to exhibit polynomial growth dynamics: let be the expected number of j-type cells of age less than a at time t starting from a k-type ancestor cell. Then, as where the constant C depends on a,j and k. and can be given explicitely. The proof is fairly short and simple, using elementary results from renewal theory and a Tauberian theorem for Laplace-Stieltjes transforms","PeriodicalId":341912,"journal":{"name":"Communications in Statistics. Stochastic Models","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129074681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 16
Asymptotic properties of interactive markov chains 交互马尔可夫链的渐近性质
Communications in Statistics. Stochastic Models Pub Date : 2000-01-01 DOI: 10.1080/15326340008807594
W. Stadje
{"title":"Asymptotic properties of interactive markov chains","authors":"W. Stadje","doi":"10.1080/15326340008807594","DOIUrl":"https://doi.org/10.1080/15326340008807594","url":null,"abstract":"For the stochastic version of Conlisk's interactive Markov chains, generalized to the case of infinitely many categories, we develop the “right”(Hilbert space) framework and prove stochastic and L 2-convergence to the corresponding deterministic version under mild assumptions. Furthermore, a weak convergence result for the scaled difference between the stochastic and the deterministic allocation profiles is proved","PeriodicalId":341912,"journal":{"name":"Communications in Statistics. Stochastic Models","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132649003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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