scholarly journals A Limit Property for Non-Homogeneous Markov Chain in Markov Environments

2016 ◽  
Vol 06 (01) ◽  
pp. 81-87
Author(s):  
成 程
Keyword(s):  
Markov Chain ◽  
Homogeneous Markov Chain ◽  
Limit Property

Strong ergodicity for continuous-time, non-homogeneous Markov chains

1982 ◽  
Vol 19 (3) ◽  
pp. 692-694 ◽  
Author(s):  
Mark Scott ◽  
Barry C. Arnold ◽  
Dean L. Isaacson
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Continuous Time ◽  
Homogeneous Markov Chain ◽  
Strong Ergodicity

Characterizations of strong ergodicity for Markov chains using mean visit times have been found by several authors (Huang and Isaacson (1977), Isaacson and Arnold (1978)). In this paper a characterization of uniform strong ergodicity for a continuous-time non-homogeneous Markov chain is given. This extends the characterization, using mean visit times, that was given by Isaacson and Arnold.

scholarly journals The local limit theorem for sums of random variables defined on a homogeneous Markov chain in the case of the stable limit distribution law

1961 ◽  
Vol 1 (1-2) ◽  
pp. 7-16
Author(s):  
A. Aleškevičienė
Keyword(s):  
Markov Chain ◽  
Limit Theorem ◽  
Limit Distribution ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Homogeneous Markov Chain ◽  
Stable Limit ◽  
Distribution Law ◽  
Sums Of Random Variables ◽  
Stable Limit Distribution

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: A. Алешкявичене. Локальная предельная теорема для сумм случайных величин, связанных в однородную цепь Маркова в случае устойчивого предельного распределения A. Aleškevičienė. Lokalinė ribinė teorema atsitiktinių dydžių, surištų homogenine Markovo grandine, sumoms stabilaus ribinio dėsnio atveju  

On the limiting behaviour of a non-homogeneous Markovian manpower model with independent Poisson input

1982 ◽  
Vol 19 (2) ◽  
pp. 433-438 ◽  
Author(s):  
P.-C. G. Vassiliou
Keyword(s):  
Markov Chain ◽  
Markov Chain Model ◽  
Random Variable ◽  
Homogeneous Markov Chain ◽  
Chain Model ◽  
Poisson Random Variable ◽  
Poisson Input ◽  
Manpower System ◽  
Limiting Behaviour ◽  
Mutually Independent

We study the limiting behaviour of a manpower system where the non-homogeneous Markov chain model proposed by Young and Vassiliou (1974) is applicable. This is done in the cases where the input is a time-homogeneous and time-inhomogeneous Poisson random variable. It is also found that the number in the various grades are asymptotically mutually independent Poisson variates.

Risk assessment for financial accounting: modeling probability of default

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Tobias Filusch
Keyword(s):  
Markov Chain ◽  
Business Cycle ◽  
Markov Chain Model ◽  
Accounting Standards ◽  
Financial Accounting ◽  
Homogeneous Markov Chain ◽  
Chain Model ◽  
Probability Of Default ◽  
Content Type ◽  
Term Structures

Purpose This paper aims to introduce and tests models for point-in-time probability of default (PD) term structures as required by international accounting standards. Corresponding accounting standards prescribe that expected credit losses (ECLs) be recognized for the impairment of financial instruments, for which the probability of default strongly embodies the included default risk. This paper fills the research gap resulting from a lack of models that expand upon existing risk management techniques, link PD term structures of different risk classes and are compliant with accounting standards, e.g. offering the flexibility for business cycle-related variations. Design/methodology/approach The author modifies the non-homogeneous continuous-time Markov chain model (NHCTMCM) by Bluhm and Overbeck (2007a, 2007b) and introduces the generalized through-the-cycle model (GTTCM), which generalizes the homogeneous Markov chain approach to a point-in-time model. As part of the overall ECL estimation, an empirical study using Standard and Poor’s (S&P) transition data compares the performance of these models using the mean squared error. Findings The models can reflect observed PD term structures associated with different time periods. The modified NHCTMCM performs best at the expense of higher complexity and only its cumulative PD term structures can be transferred to valid ECL-relevant unconditional PD term structures. For direct calibration to these unconditional PD term structures, the GTTCM is only slightly worse. Moreover, it requires only half of the number of parameters that its competitor does. Both models are useful additions to the implementation of accounting regulations. Research limitations/implications The tests are only carried out for 15-year samples within a 35-year span of available S&P transition data. Furthermore, a point-in-time forecast of the PD term structure requires a link to the business cycle, which seems difficult to find, but is in principle necessary corresponding to the accounting requirements. Practical implications Research findings are useful for practitioners, who apply and develop the ECL models of financial accounting. Originality/value The innovative models expand upon the existing methodologies for assessing financial risks, motivated by the practical requirements of new financial accounting standards.

On the limiting behaviour of a non-homogeneous Markovian manpower model with independent Poisson input

1982 ◽  
Vol 19 (02) ◽  
pp. 433-438 ◽  
Author(s):  
P.-C. G. Vassiliou
Keyword(s):  
Markov Chain ◽  
Markov Chain Model ◽  
Random Variable ◽  
Homogeneous Markov Chain ◽  
Chain Model ◽  
Poisson Random Variable ◽  
Poisson Input ◽  
Manpower System ◽  
Limiting Behaviour ◽  
Mutually Independent

We study the limiting behaviour of a manpower system where the non-homogeneous Markov chain model proposed by Young and Vassiliou (1974) is applicable. This is done in the cases where the input is a time-homogeneous and time-inhomogeneous Poisson random variable. It is also found that the number in the various grades are asymptotically mutually independent Poisson variates.

Path planning for intelligent robot based on switching local evolutionary PSO algorithm

2016 ◽  
Vol 36 (2) ◽  
pp. 120-126 ◽  
Author(s):  
Nianyin Zeng ◽  
Hong Zhang ◽  
Yanping Chen ◽  
Binqiang Chen ◽  
Yurong Liu
Keyword(s):  
Markov Chain ◽  
Path Planning ◽  
Three Dimensional ◽  
Grid Method ◽  
Pso Algorithm ◽  
Planning Problem ◽  
Homogeneous Markov Chain ◽  
Intelligent Robot ◽  
Environment Modeling ◽  
Content Type

Purpose This paper aims to present a novel particle swarm optimization (PSO) based on a non-homogeneous Markov chain and differential evolution (DE) for path planning of intelligent robot when having obstacles in the environment. Design/methodology/approach The three-dimensional path surface of the intelligent robot is decomposed into a two-dimensional plane and the height information in z axis. Then, the grid method is exploited for the environment modeling problem. After that, a recently proposed switching local evolutionary PSO (SLEPSO) based on non-homogeneous Markov chain and DE is analyzed for the path planning problem. The velocity updating equation of the presented SLEPSO algorithm jumps from one mode to another based on the non-homogeneous Markov chain, which can overcome the contradiction between local and global search. In addition, DE mutation and crossover operations can enhance the capability of finding a better global best particle in the PSO method. Findings Finally, the SLEPSO algorithm is successfully applied to the path planning in two different environments. Comparing with some well-known PSO algorithms, the experiment results show the feasibility and effectiveness of the presented method. Originality/value Therefore, this can provide a new method for the area of path planning of intelligent robot.

Reduction techniques for discrete-time Markov chains on totally ordered state space using stochastic comparisons

2000 ◽  
Vol 37 (03) ◽  
pp. 795-806 ◽  
Author(s):  
Laurent Truffet
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
Discrete Time ◽  
Stochastic Comparison ◽  
Homogeneous Markov Chain ◽  
Monotone Functions ◽  
Stochastic Comparisons ◽  
Reduction Techniques ◽  
Ordered State

We propose in this paper two methods to compute Markovian bounds for monotone functions of a discrete time homogeneous Markov chain evolving in a totally ordered state space. The main interest of such methods is to propose algorithms to simplify analysis of transient characteristics such as the output process of a queue, or sojourn time in a subset of states. Construction of bounds are based on two kinds of results: well-known results on stochastic comparison between Markov chains with the same state space; and the fact that in some cases a function of Markov chain is again a homogeneous Markov chain but with smaller state space. Indeed, computation of bounds uses knowledge on the whole initial model. However, only part of this data is necessary at each step of the algorithms.

On the optimization of free resources using non-homogeneous Markov chain software rejuvenation model

2007 ◽  
Vol 92 (12) ◽  
pp. 1724-1732 ◽  
Author(s):  
Vasilis P. Koutras ◽  
Agapios N. Platis ◽  
George A. Gravvanis
Keyword(s):  
Markov Chain ◽  
Homogeneous Markov Chain ◽  
Software Rejuvenation
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