On a class of one-dimensional Markov processes with continuous paths

2007 ◽  
pp. 131-142
Author(s):  
Nobuyuki Ikeda ◽  
Yukio Ogura
Keyword(s):  
Markov Processes ◽  
One Dimensional

scholarly journals Development of the logical part of the intellectual multi-parameter relay protection

2019 ◽  
Vol 139 ◽  
pp. 01060 ◽  
Author(s):  
Anton Loskutov ◽  
Pavel Pelevin ◽  
Mile Mitrovoc
Keyword(s):  
Markov Processes ◽  
Software Package ◽  
Statistical Data ◽  
Reactive Power ◽  
Relay Protection ◽  
One Dimensional ◽  
Active And Reactive Power ◽  
Logical Part ◽  
Fault Detectors

The issues of increasing the sensitivity and reliability of multi-parameter relay protection by sharing more than one information feature (current module, voltage module and phase, active and reactive power) are considered. In this case, the response parameters of individual one-dimensional measuring fault detectors based on the accumulation of statistical data during simulation in the Matlab / Similink software package are determined. A method for combining the signals of one-dimensional measuring fault detectors to increase the sensitivity of protection is proposed. The reliability of the organization of the logical part of multi-parameter relay protection was estimated using the theory of Markov processes, the principles of “2 out of 3” and “1 out of 2”.

A comparison theorem for conditioned Markov processes

1991 ◽  
Vol 28 (01) ◽  
pp. 74-83 ◽  
Author(s):  
G. O. Roberts
Keyword(s):  
Markov Processes ◽  
Comparison Theorem ◽  
Hitting Time ◽  
Time Dependent ◽  
One Dimensional

Intuitively, the effect of conditioning a one-dimensional process to remain below a certain (possibly time-dependent) boundary is to ‘push' the process downwards. This paper investigates the effect of such conditioning, and finds the class of processes for which our intuition is accurate. It is found that ordinary stochastic inequalities are in general unsuitable for making statements about such conditioned processes, and that a stronger type of inequality is more appropriate. The investigation is motivated by applications in estimation of boundary hitting time distributions.

Ergodicity of diffusion and temporal uniformity of diffusion approximation

1977 ◽  
Vol 14 (02) ◽  
pp. 399-404 ◽  
Author(s):  
M. Frank Norman
Keyword(s):  
Markov Processes ◽  
Diffusion Approximation ◽  
Genetic Models ◽  
Auxiliary Condition ◽  
One Dimensional ◽  
Continuous Parameter

Let {XN (t), t ≧ 0}, N = 1, 2, … be a sequence of continuous-parameter Markov processes, and let TN (t)f(x) = Ex [f(XN (t))]. Suppose that limN→∞ T N (t)f(x)= T(t)f(x), and that convergence is uniform over x and over t ∈ [0, K] for all K < ∞. When is convergence uniform over t ∈ [0, ∞)? Questions of this type are considered under the auxiliary condition that T(t)f(x) converges uniformly over x as t → ∞. A criterion for such ergodicity is given for semigroups T(t) associated with one-dimensional diffusions. The theory is illustrated by applications to genetic models.

Strong ergodicity for Markov processes by coupling methods

2002 ◽  
Vol 39 (4) ◽  
pp. 839-852 ◽  
Author(s):  
Yong-Hua Mao
Keyword(s):  
Markov Processes ◽  
Sufficient Conditions ◽  
Essential Spectra ◽  
Strong Ergodicity ◽  
One Dimensional ◽  
Coupling Methods ◽  
Explicit Criteria ◽  
Birth Death

In this paper, we apply coupling methods to study strong ergodicity for Markov processes, and sufficient conditions are presented in terms of the expectations of coupling times. In particular, explicit criteria are obtained for one-dimensional diffusions and birth-death processes to be strongly ergodic. As a by-product, strong ergodicity implies that the essential spectra of the generators for these processes are empty.

Large overshoots of one-dimensional markov processes

1981 ◽  
Vol 24 (10) ◽  
pp. 854-856
Author(s):  
A. L. Virovlyanskii ◽  
A. N. Malakhov
Keyword(s):  
Markov Processes ◽  
One Dimensional
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