共查询到20条相似文献,搜索用时 296 毫秒
1.
V. S. Korolyuk 《Ukrainian Mathematical Journal》2005,57(9):1442-1465
We propose a system approach to the asymptotic analysis of stochastic systems in the scheme of series with averaging and diffusion
approximation. Stochastic systems are defined by Markov processes with locally independent increments in a Euclidean space
with random switchings that are described by jump Markov and semi-Markov processes. We use the asymptotic analysis of Markov
and semi-Markov random evolutions. We construct the diffusion approximation using the asymptotic decomposition of generating
operators and solutions of problems of singular perturbation for reducibly inverse operators.
__________
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 9, pp. 1235–1252, September, 2005. 相似文献
2.
We propose an approach to the proof of the weak convergence of a semi-Markov process to a Markov process under certain conditions
imposed on local characteristics of the semi-Markov process. 相似文献
3.
Amogh Deshpande 《随机分析与应用》2013,31(6):911-933
The finite state semi-Markov process is a generalization over the Markov chain in which the sojourn time distribution is any general distribution. In this article, we provide a sufficient stochastic maximum principle for the optimal control of a semi-Markov modulated jump-diffusion process in which the drift, diffusion, and the jump kernel of the jump-diffusion process is modulated by a semi-Markov process. We also connect the sufficient stochastic maximum principle with the dynamic programming equation. We apply our results to finite horizon risk-sensitive control portfolio optimization problem and to a quadratic loss minimization problem. 相似文献
4.
B. P. Harlamov 《Journal of Mathematical Sciences》2010,167(4):574-587
A continuous semi-Markov process with values in a closed interval is considered. This process coincides with a Markov diffusion
process inside the interval. Thus, violation of the Markov property is only possible at the boundary of the interval. We prove
a sufficient condition under which a semi-Markov process is Markov. We show that, in addition to Markov processes with instantaneous
reflection from the boundary of the interval. there exists a class of Markov processes with delayed reflection from the boundary.
Such a process has a positive average measure of time at which its trajectory belongs to the boundaries. This gives a different
proof of a similar result by Gikhman and Skorokhod of 1968. Bibliography: 5 titles. 相似文献
5.
Yann Gudon 《商业与工业应用随机模型》1999,15(3):195-224
We propose a computational approach for implementing discrete hidden semi-Markov chains. A discrete hidden semi-Markov chain is composed of a non-observable or hidden process which is a finite semi-Markov chain and a discrete observable process. Hidden semi-Markov chains possess both the flexibility of hidden Markov chains for approximating complex probability distributions and the flexibility of semi-Markov chains for representing temporal structures. Efficient algorithms for computing characteristic distributions organized according to the intensity, interval and counting points of view are described. The proposed computational approach in conjunction with statistical inference algorithms previously proposed makes discrete hidden semi-Markov chains a powerful model for the analysis of samples of non-stationary discrete sequences. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
6.
Yu. E. Obzherin A. I. Peschanskii A. V. Skatkov 《Journal of Mathematical Sciences》1994,72(5):3316-3319
A semi-Markov process with a discrete-continuous phase space is applied to describe a renewal process with switching. Formulas are derived for the stationary distribution of the embedded Markov chain and the stationary characteristics of the system.Sevastopol' Instrument-Building Institute. Translated from Dinamicheskie Sistemy, No. 10, pp. 63–68, 1992. 相似文献
7.
A rigorous definition of semi-Markov dependent risk model is given. This model is a generalization of the Markov dependent risk model. A criterion and necessary conditions of semi- Markov dependent risk model are obtained. The results clarify relations between elements among semi-Markov dependent risk model more clear and are applicable for Markov dependent risk model. 相似文献
8.
V. S. Koroliuk V. V. Koroliuk N. Limnios 《Methodology and Computing in Applied Probability》2009,11(2):201-209
We study asymptotic average and diffusion approximation schemes for semi-Markov queuing systems by a random evolution approach
and using compensating operator of the corresponding extended Markov renewal process. These results generalize Markov and
renewal flow queuing systems.
相似文献
9.
The literature about maximum of entropy for Markov processes deals mainly with discrete-time Markov chains. Very few papers dealing with continuous-time jump Markov processes exist and none dealing with semi-Markov processes. It is the aim of this paper to contribute to fill this lack. We recall the basics concerning entropy for Markov and semi-Markov processes and we study several problems to give an overview of the possible directions of use of maximum entropy in connection with these processes. Numeric illustrations are presented, in particular in application to reliability. 相似文献
10.
V. V. Korolyuk 《Ukrainian Mathematical Journal》1991,43(1):111-114
The central limit theorem for nonhomogeneous processes with independent increments with semi-Markov switchings with a uniformly ergodic imbedded Markov chain is proved.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 1, pp. 134–137, January, 1991. 相似文献
11.
B. P. Harlamov 《Journal of Mathematical Sciences》2008,152(6):958-965
A continuous semi-Markov process with a segment as the range of values is considered. This process coincides with a diffusion
process inside the segment, i.e., up to the first hitting time of the boundary of the segment and at any time when the process
leaves the boundary. The class of such processes consists of Markov processes with reflection at the boundaries (instantaneously
or with a delay) and semi-Markov processes with intervals of constancy on some boundary. We derive conditions of existence
of such a process in terms of a semi-Markov transition generating function on the boundary. The method of imbedded alternating
renewal processes is applied to find a stationary distribution of the process. Bibliography: 3 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 351, 2007, pp. 284–297. 相似文献
12.
Limit theorems for functionals of classical (homogeneous) Markov renewal and semi-Markov processes have been known for a long time, since the pioneering work of Pyke Schaufele (Limit theorems for Markov renewal processes, Ann. Math. Statist., 35(4):1746–1764, 1964). Since then, these processes, as well as their time-inhomogeneous generalizations, have found many applications, for example, in finance and insurance. Unfortunately, no limit theorems have been obtained for functionals of inhomogeneous Markov renewal and semi-Markov processes as of today, to the best of the authors’ knowledge. In this article, we provide strong law of large numbers and central limit theorem results for such processes. In particular, we make an important connection of our results with the theory of ergodicity of inhomogeneous Markov chains. Finally, we provide an application to risk processes used in insurance by considering a inhomogeneous semi-Markov version of the well-known continuous-time Markov chain model, widely used in the literature. 相似文献
13.
We present a method for the derivation of second-order moment equations for solutions of a system of nonlinear equations that depends on a finite-valued semi-Markov or Markov process. For systems of linear differential equations with random coefficients, the case where the inhomogeneous part contains white noise is considered.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 5, pp. 687–690, May, 2004. 相似文献
14.
This paper concerns the study of asymptotic properties of the maximum likelihood estimator (MLE) for the general hidden semi-Markov
model (HSMM) with backward recurrence time dependence. By transforming the general HSMM into a general hidden Markov model,
we prove that under some regularity conditions, the MLE is strongly consistent and asymptotically normal. We also provide
useful expressions for asymptotic covariance matrices, involving the MLE of the conditional sojourn times and the embedded
Markov chain of the hidden semi-Markov chain. Bibliography: 17 titles. 相似文献
15.
V. S. Korolyuk 《Journal of Mathematical Sciences》1987,38(5):2299-2308
One presents the results obtained recently by the collaborators of the Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, regarding limit theorems for additive functionals of Markov and semi-Markov processes. One makes use of the theory of inversion of singularly perturbed semigroups of operators in the phase extension scheme and of the methods of asymptotic analysis of singularly perturbed Markov renewal equations.Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 229–246, 1986. 相似文献
16.
A. O. Pohorui 《Ukrainian Mathematical Journal》2010,62(2):210-221
We investigate asymptotic expansions of solutions of singularly perturbed transport equations in Markov and semi-Markov media. 相似文献
17.
We study stochastic processes with age-dependent transition rates. A typical example of such a process is a semi-Markov process which is completely determined by the holding time distributions in each state and the transition probabilities of the embedded Markov chain. The process we construct generalizes semi-Markov processes. One important feature of this process is that unlike semi-Markov processes the transition probabilities of this process are age-dependent. Under certain condition we establish the Feller property of the process. Finally, we compute the limiting distribution of the process. 相似文献
18.
V. K. Malinovskii 《Journal of Mathematical Sciences》1987,36(4):493-502
For Harris recurrent Markov renewal processes and semi-Markov processes one obtains a central limit theorem. One also obtains Berry-Esseen type estimates for this theorem. Their proof is based on the Kolmogorov-Doeblin regenerative method.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 142, pp. 86–97, 1985. 相似文献
19.
This work studies the threshold dynamics and ergodicity of a stochastic SIRS epidemic model with the disease transmission rate driven by a semi-Markov process. The semi-Markov process used in this paper for describing a randomly changing environment is a very large extension of the most common Markov regime-switching process. We define a basic reproduction number for the semi-Markov regime-switching environment and show that its position with respect to 1 determines the extinction or persistence of the disease. In the case of disease persistence, we give mild sufficient conditions for ensuring the existence and absolute continuity of the invariant probability measure. Under the same conditions, we also prove the global attractivity of the Ω-limit set of the system and the convergence in total variation norm of the transition probability to the invariant measure. Compared with the existing results in the Markov regime-switching environment, the results generalized require almost no additional conditions. 相似文献
20.
The problem of estimating the Markov renewal matrix and the semi-Markov transition matrix based on a history of a finite semi-Markov
process censored at time T (fixed) is addressed for the first time. Their asymptotic properties are studied. We begin by the definition of the transition
rate of this process and propose a maximum likelihood estimator for the hazard rate functions and then we show that this estimator
is uniformly strongly consistent and converges weakly to a normal random variable. We construct a new estimator for an absolute
continous semi-Markov kernel and give detailed derivation of uniform strong consistency and weak convergence of this estimator
as the censored time tends to infinity.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献