scholarly journals Determining the time scale of a Markov chain

1964 ◽  
Vol 15 (1) ◽  
pp. 87-87
Author(s):  
David A. Freedman
Keyword(s):  
2011 ◽  
Vol 52 (4) ◽  
pp. 372-390
Author(s):  
DUNG TIEN NGUYEN ◽  
XUERONG MAO ◽  
G. YIN ◽  
CHENGGUI YUAN

AbstractThis paper considers singular systems that involve both continuous dynamics and discrete events with the coefficients being modulated by a continuous-time Markov chain. The underlying systems have two distinct characteristics. First, the systems are singular, that is, characterized by a singular coefficient matrix. Second, the Markov chain of the modulating force has a large state space. We focus on stability of such hybrid singular systems. To carry out the analysis, we use a two-time-scale formulation, which is based on the rationale that, in a large-scale system, not all components or subsystems change at the same speed. To highlight the different rates of variation, we introduce a small parameter ε>0. Under suitable conditions, the system has a limit. We then use a perturbed Lyapunov function argument to show that if the limit system is stable then so is the original system in a suitable sense for ε small enough. This result presents a perspective on reduction of complexity from a stability point of view.


2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jie Liu ◽  
Xingquan Ji ◽  
Kejun Li ◽  
Kaiyuan Zhang

A multi-time scale optimal dispatch model based on the scenario method and model predictive control (MPC) in the AC/DC distribution network is established due to the uncertainty of wind and load. A Markov chain dynamic scenario method is proposed, which generates scenarios by characterizing the forecast error via empirical distribution. Considering the time correlation of the forecast error, Markov chain is adopted in the Markov chain dynamic method to simulate the uncertainty and variability in wind and load with time. A multi-time scale optimal dispatch strategy based on MPC is proposed. The operation scheduling of operation units is solved in day-ahead and intraday optimal dispatch by minimizing the expected value of total cost in each scenario. In the real-time optimal dispatch, the stability and robustness of system operation are considered. MPC is adopted in the real-time optimal dispatch, taking the intraday scheduling as reference and using the roll optimization method to compute real-time optimal dispatch scheduling to smooth the output power. The simulation results in a 50-node system with uncontrollable distributed energy demonstrate that the proposed model and strategy can effectively eliminate fluctuations in wind and load in AC/DC distribution networks.


2000 ◽  
Vol 179 ◽  
pp. 205-208
Author(s):  
Pavel Ambrož ◽  
Alfred Schroll

AbstractPrecise measurements of heliographic position of solar filaments were used for determination of the proper motion of solar filaments on the time-scale of days. The filaments have a tendency to make a shaking or waving of the external structure and to make a general movement of whole filament body, coinciding with the transport of the magnetic flux in the photosphere. The velocity scatter of individual measured points is about one order higher than the accuracy of measurements.


1984 ◽  
Vol 75 ◽  
pp. 599-602
Author(s):  
T.V. Johnson ◽  
G.E. Morfill ◽  
E. Grun

A number of lines of evidence suggest that the particles making up the E-ring are small, on the order of a few microns or less in size (Terrile and Tokunaga, 1980, BAAS; Pang et al., 1982 Saturn meeting; Tucson, AZ). This suggests that a variety of electromagnetic and plasma affects may be important in considering the history of such particles. We have shown (Morfill et al., 1982, J. Geophys. Res., in press) that plasma drags forces from the corotating plasma will rapidly evolve E-ring particle orbits to increasing distance from Saturn until a point is reached where radiation drag forces acting to decrease orbital radius balance this outward acceleration. This occurs at approximately Rhea's orbit, although the exact value is subject to many uncertainties. The time scale for plasma drag to move particles from Enceladus' orbit to the outer E-ring is ~104yr. A variety of effects also act to remove particles, primarily sputtering by both high energy charged particles (Cheng et al., 1982, J. Geophys. Res., in press) and corotating plasma (Morfill et al., 1982). The time scale for sputtering away one micron particles is also short, 102 - 10 yrs. Thus the detailed particle density profile in the E-ring is set by a competition between orbit evolution and particle removal. The high density region near Enceladus' orbit may result from the sputtering yeild of corotating ions being less than unity at this radius (e.g. Eviatar et al., 1982, Saturn meeting). In any case, an active source of E-ring material is required if the feature is not very ephemeral - Enceladus itself, with its geologically recent surface, appears still to be the best candidate for the ultimate source of E-ring material.


2019 ◽  
Vol 62 (3) ◽  
pp. 577-586 ◽  
Author(s):  
Garnett P. McMillan ◽  
John B. Cannon

Purpose This article presents a basic exploration of Bayesian inference to inform researchers unfamiliar to this type of analysis of the many advantages this readily available approach provides. Method First, we demonstrate the development of Bayes' theorem, the cornerstone of Bayesian statistics, into an iterative process of updating priors. Working with a few assumptions, including normalcy and conjugacy of prior distribution, we express how one would calculate the posterior distribution using the prior distribution and the likelihood of the parameter. Next, we move to an example in auditory research by considering the effect of sound therapy for reducing the perceived loudness of tinnitus. In this case, as well as most real-world settings, we turn to Markov chain simulations because the assumptions allowing for easy calculations no longer hold. Using Markov chain Monte Carlo methods, we can illustrate several analysis solutions given by a straightforward Bayesian approach. Conclusion Bayesian methods are widely applicable and can help scientists overcome analysis problems, including how to include existing information, run interim analysis, achieve consensus through measurement, and, most importantly, interpret results correctly. Supplemental Material https://doi.org/10.23641/asha.7822592


2020 ◽  
pp. 35-38
Author(s):  
S.I. Donchenko ◽  
I.Y. Blinov ◽  
I.B. Norets ◽  
Y.F. Smirnov ◽  
A.A. Belyaev ◽  
...  

The latest changes in the algorithm for the formation of the international atomic time scale TAI are reported in terms of estimating the weights of the clocks involved in the formation of TAI. Studies of the characteristics of the long-term instability of new-generation hydrogen masers based on processing the results of the clock frequency difference with respect to TAI are performed. It has been confirmed that at present, new-generation hydrogen masers show significantly less long-term instability in comparison with quantum frequency standards ofsimilar and other types.


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