Markov process

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1. A Markov process is a random process in which the future is independent of the past, given the present.
2. Thus, Markov processes are the natural stochastic analogs of the deterministic processes described by differential and difference equations.
3. Sometimes the term Markov process is restricted to sequences in which the random variables can assume continuous values, and analogous sequences of discrete-valued variables are called Markov chains.
4. The defining property of a Markov process is commonly called the Markov property; it was first stated by A.A. Markov .
5. Examples of continuous-time Markov processes are furnished by diffusion processes (cf.
6. Then the corresponding Markov process can be taken to be right-continuous and having left limits (that is, its trajectories can be chosen so).
7. In the theory of Markov processes most attention is given to homogeneous (in time) processes.
8. A Markov process with stationary transition probabilities may or may not be a stationary process in the sense of the preceding paragraph.
9. If the Ys are identically distributed as well as independent, this transition probability does not depend on t, and then X(t) is a Markov process with stationary transition probabilities.
10. Since both the Poisson process and Brownian motion are created from random walks by simple limiting processes, they, too, are Markov processes with stationary transition probabilities.
11. The Ornstein-Uhlenbeck process defined as the solution (19) to the stochastic differential equation (18) is also a Markov process with stationary transition probabilities.
12. The connection between the Markov processes and certain linear equations is now well understood and can be explained in many ways.
13. We continue by constructing a similar semigroup using Markov processes.
14. and therefore, the infinitesimal operators of Markov processes do not contain any zeroth-order terms.
15. Each number represents the probability of the Markov process changing from one state to another state, with the direction indicated by the arrow.
16. In addition, there are other extensions of Markov processes that are referred to as such but do not necessarily fall within any of these four categories (see Markov model).
17. However, it is possible to model this scenario as a Markov process.
18. Markov chains and continuous-time Markov processes are useful in chemistry when physical systems closely approximate the Markov property.
19. When the range of possible values for a i is either finite or infinite denumerable, as in this study, the Markov process may be referred as a Markov chain.
20. A first-order Markov process is a Markov process where the transition from a class to any other does not require intermediate transitions to other states.
21. As described in the methodology, the main hypothesis to be tested in this study is that LUCC in the study area is generated by a first order Markov process.
22. To prove H 0 two subsidiary hypotheses must be verified: H 1 - land use/cover in different time periods is not statistically independent and H 2 - LUCC in the study area is a Markov process.
23. The first correct mathematical construction of a Markov process with continuous trajectories was given by N. WIENER in 1923.
24. The general theory of Markov processes was developed in the 1930's and 1940's by A. N. KOL­ MOGOROV, W. FELLER, W. DOEBLlN, P. LEVY, J. L. DOOB, and others.
25. During the past ten years the theory of Markov processes has entered a new period of intensive development.
26. The methods of the theory of semigroups of linear operators made possible further progress in the classification of Markov processes by their infinitesimal characteristics.
27. The book begins with a review of basic probability, then covers the case of finite state, discrete time Markov processes.
28. Building on this, the text deals with the discrete time, infinite state case and provides background for continuous Markov processes with exponential random variables and Poisson processes.
29. It presents continuous Markov processes which include the basic material of Kolmogorov’s equations, infinitesimal generators, and explosions.
30. While Markov processes are touched on in probability courses, this book offers the opportunity to concentrate on the topic when additional study is required.
31. But in literature, several empirical evidences suggest that Markov process is not appropriate for credit rating process.
32. In the present paper the importance of Markov process is shown by analysing the reliability function and availability of feeding system of sugar industry.
33. To investigate these complex repairable systems various tools such as Markov process, semi-Markov, Petri nets, and dynamic FTA are developed.
34. Hence system involving Markov process is considered in this discussion with certain assumptions.
35. Thus the performance of a repairable system can be easily analysed by exhibiting time-homogeneous Markov process and modelling its finite states.
36. In this work it is proposed a model for the assessment of availability measure of fault tolerant systems based on the integration of continuous time semi-Markov processes and Bayesian belief networks.
37. It is also proposed a numerical procedure for the solution of the state probability equations of semi-Markov processes described in terms of transition rates.
38. (2004) who use semi-Markov processes to model a possible security intrusion and corresponding response of the fault tolerant software system to this event.
39. (1994) and Chandra & Kumar (1997) use Markov processes (MP) in order to model safety systems with stochastic TDTs.
40. The module first introduces the theory of Markov processes with continuous time parameter running on graphs.
41. In order to solve this problem we make use of Markov chains or Markov processes (which are a special type of stochastic process).
42. To consolidate your knowledge of Markov processes consider the following example.
43. One interesting application of Markov processes that I know of concerns the Norwegian offshore oil/gas industry.
44. To overcome this problem they model oil price as a Markov process with three price levels (states), corresponding to optimistic, most likely and pessimistic scenarios.
45. We consider a general homogeneous continuous-time Markov process with restarts.
46. We provide a connection between the transition probability functions of the original Markov process and the modified process with restarts.
47. This paper presents a Markov process–based method for deterioration prediction of building components using condition data collected by the City of Kingston in Australia.
48. The paper presents a typical decision-making method based on the Markov process.
49. Transitions in LAMP may be influenced by states visited in the distant history of the process, but unlike higher-order Markov processes, LAMP retains an efficient parameterization.
50. Martingale problems for general Markov processes are systematically developed for the first time in book form.
51. The linking model for all these examples is the Markov process, which includes random walk, Markov chain and Markov jump processes.

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• [{'LOWER': 'markov'}, {'LEMMA': 'process'}]