An infinite variance solidarity theorem for Markov renewal functions

1996 ◽  
Vol 33 (02) ◽  
pp. 434-438 ◽  
Author(s):  
M. S. Sgibnev
Keyword(s):  
Renewal Process ◽  
Expected Value ◽  
Infinite Variance ◽  
Markov Renewal Process ◽  
Initial Moment ◽  
Recurrence Times ◽  
The Mean

Let , be a recurrent Markov renewal process and Mik (t) be the expected value of Nk (t) provided that at the initial moment the system is in state i. It is shown that when the mean recurrence times μ ii are finite, the differences μ ij Mki (t) – t behave asymptotically the same for all states i and k.

An infinite variance solidarity theorem for Markov renewal functions

1996 ◽  
Vol 33 (2) ◽  
pp. 434-438 ◽  
Author(s):  
M. S. Sgibnev
Keyword(s):  
Renewal Process ◽  
Expected Value ◽  
Infinite Variance ◽  
Markov Renewal Process ◽  
Initial Moment ◽  
Recurrence Times ◽  
The Mean

Let , be a recurrent Markov renewal process and Mik(t) be the expected value of Nk(t) provided that at the initial moment the system is in state i. It is shown that when the mean recurrence times μ ii are finite, the differences μ ij Mki (t) – t behave asymptotically the same for all states i and k.

MR/GI/1 queues by positively correlated arrival stream

1994 ◽  
Vol 31 (02) ◽  
pp. 497-514
Author(s):  
R. Szekli ◽  
R. L. Disney ◽  
S. Hur
Keyword(s):  
Renewal Process ◽  
Point Processes ◽  
Waiting Times ◽  
Jump Process ◽  
Arrival Process ◽  
Markov Renewal Process ◽  
Stochastic Comparison ◽  
Single Server ◽  
Comparison Results ◽  
The Mean

The effects of dependencies (such as association) in the arrival process to a single server queue on mean queue lengths and mean waiting times are studied. Markov renewal arrival processes with a particular transition matrix for the underlying Markov chain are used which allow us to change dependency properties without at the same time changing distributional conditions. It turns out that correlations do not seem to be pure effects, and three main factors are studied: (a) differences in the mean interarrival times in the underlying Markov renewal process, (b) intensity in the Markov renewal jump process, (c) variability in the point processes underlying the Markov renewal process. It is shown that the mean queue length can be made arbitrarily large in the class of queues with the same interarrival distributions and the same service time distributions (with fixed smaller than one traffic intensity), by making (a) large enough and (b) small enough. The existence of the moments of interest is confirmed and some stochastic comparison results for actual waiting times are shown.

Traffic noise as a filtered Markov renewal process

1973 ◽  
Vol 10 (02) ◽  
pp. 377-386 ◽  
Author(s):  
Allan H. Marcus
Keyword(s):  
Renewal Process ◽  
Noise Level ◽  
Traffic Noise ◽  
Engineering Practice ◽  
Markov Renewal Process ◽  
Noise Emission ◽  
Mean And Variance ◽  
Explicit Formulae ◽  
The Mean ◽  
Modest Degree

Traffic noise depends significantly on statistical properties of highway flow. The noise heard by an off-highway observer is the sum of the contributions of all the vehicles on the highway. We assume that vehicle spacings on a single-lane infinite straight road form a Markov renewal process (MRP) with N states or vehicle types. The noise impact is then a two-sided filtered MRP. We give explicit formulae for the mean and variance in the case N = 2 and exponential headways. Jewell's (1965) study (cars vs. trucks in the southbound curb lane of U.S. 40) gives parameters of the MPR for a numerical example. Even with only a modest degree of truck clustering and variability in vehicle spacings and noise emission, the variation in noise level is much greater than usually predicted. The coefficient of variation of arithmetic noise intensity is greater than unity at distances from the roadway less than 700 feet. The logarithmic noise level parameters L 50 and L 10 usually computed in engineering practice may be in error by 2 to 3 decibels if these sources of variability are ignored.

Traffic noise as a filtered Markov renewal process

1973 ◽  
Vol 10 (2) ◽  
pp. 377-386 ◽  
Author(s):  
Allan H. Marcus
Keyword(s):  
Renewal Process ◽  
Noise Level ◽  
Traffic Noise ◽  
Engineering Practice ◽  
Markov Renewal Process ◽  
Noise Emission ◽  
Mean And Variance ◽  
Explicit Formulae ◽  
The Mean ◽  
Modest Degree

Traffic noise depends significantly on statistical properties of highway flow. The noise heard by an off-highway observer is the sum of the contributions of all the vehicles on the highway. We assume that vehicle spacings on a single-lane infinite straight road form a Markov renewal process (MRP) with N states or vehicle types. The noise impact is then a two-sided filtered MRP. We give explicit formulae for the mean and variance in the case N = 2 and exponential headways. Jewell's (1965) study (cars vs. trucks in the southbound curb lane of U.S. 40) gives parameters of the MPR for a numerical example. Even with only a modest degree of truck clustering and variability in vehicle spacings and noise emission, the variation in noise level is much greater than usually predicted. The coefficient of variation of arithmetic noise intensity is greater than unity at distances from the roadway less than 700 feet. The logarithmic noise level parameters L50 and L10 usually computed in engineering practice may be in error by 2 to 3 decibels if these sources of variability are ignored.

MR/GI/1 queues by positively correlated arrival stream

1994 ◽  
Vol 31 (2) ◽  
pp. 497-514 ◽  
Author(s):  
R. Szekli ◽  
R. L. Disney ◽  
S. Hur
Keyword(s):  
Renewal Process ◽  
Point Processes ◽  
Waiting Times ◽  
Jump Process ◽  
Arrival Process ◽  
Markov Renewal Process ◽  
Stochastic Comparison ◽  
Single Server ◽  
Comparison Results ◽  
The Mean

The effects of dependencies (such as association) in the arrival process to a single server queue on mean queue lengths and mean waiting times are studied. Markov renewal arrival processes with a particular transition matrix for the underlying Markov chain are used which allow us to change dependency properties without at the same time changing distributional conditions. It turns out that correlations do not seem to be pure effects, and three main factors are studied: (a) differences in the mean interarrival times in the underlying Markov renewal process, (b) intensity in the Markov renewal jump process, (c) variability in the point processes underlying the Markov renewal process. It is shown that the mean queue length can be made arbitrarily large in the class of queues with the same interarrival distributions and the same service time distributions (with fixed smaller than one traffic intensity), by making (a) large enough and (b) small enough. The existence of the moments of interest is confirmed and some stochastic comparison results for actual waiting times are shown.

scholarly journals Non-Homogeneous Semi-Markov and Markov Renewal Processes and Change of Measure in Credit Risk

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 55
Author(s):  
P.-C.G. Vassiliou
Keyword(s):  
Markov Chain ◽  
Probability Measure ◽  
Renewal Process ◽  
Markov Chain Model ◽  
Markov Renewal Process ◽  
Renewal Processes ◽  
Chain Model ◽  
Markov Renewal Processes ◽  
Risky Bonds ◽  
Markov Structure

For a G-inhomogeneous semi-Markov chain and G-inhomogeneous Markov renewal processes, we study the change from real probability measure into a forward probability measure. We find the values of risky bonds using the forward probabilities that the bond will not default up to maturity time for both processes. It is established in the form of a theorem that the forward probability measure does not alter the semi Markov structure. In addition, foundation of a G-inhohomogeneous Markov renewal process is done and a theorem is provided where it is proved that the Markov renewal process is maintained under the forward probability measure. We show that for an inhomogeneous semi-Markov there are martingales that characterize it. We show that the same is true for a Markov renewal processes. We discuss in depth the calibration of the G-inhomogeneous semi-Markov chain model and propose an algorithm for it. We conclude with an application for risky bonds.

scholarly journals A New Approach for Analyzing the Reliability of the Repair Facility in a Series System with Vacations

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Renbin Liu ◽  
Yong Wu
Keyword(s):  
Renewal Process ◽  
Decomposition Method ◽  
Process Theory ◽  
Series System ◽  
New Approach ◽  
Numerical Examples ◽  
Special Cases ◽  
The Mean ◽  
Repair Facility

Based on the renewal process theory we develop a decomposition method to analyze the reliability of the repair facility in ann-unit series system with vacations. Using this approach, we study the unavailability and the mean replacement number during(0,t]of the repair facility. The method proposed in this work is novel and concise, which can make us see clearly the structures of the facility indices of a series system with an unreliable repair facility, two convolution relations. Special cases and numerical examples are given to show the validity of our method.

scholarly journals The use of an antagonist 5-HT2a/c for depression and motor function in Parkinson' disease

2009 ◽  
Vol 67 (2b) ◽  
pp. 407-412 ◽  
Author(s):  
Antonio Luiz dos Santos Werneck ◽  
Ana Lucia Rosso ◽  
Maurice Borges Vincent
Keyword(s):  
Parkinson Disease ◽  
Motor Function ◽  
Rating Scale ◽  
Statistical Significance ◽  
Psychotic Symptoms ◽  
Initial Moment ◽  
The Mean ◽  
Group 2 ◽  
To Receive ◽  
Group 1

OBJECTIVE: To test the ability of a 5HT2a/c (trazodone) antagonist, to improve depression and motor function in Parkinson' disease (PD). METHOD: Twenty PD patients with and without depression were randomly assigned to receive trazodone (group 1) or not (group 2). They were evaluated through UPDRS and Hamilton Depression Rating Scale (HAM-D). RESULTS: For the UPDRS the mean score of group 2 was 33.1 ± 19.7 and 37.1 ± 18.0 at the end. For the group 1, the corresponding scores were 31.4 ± 11.3 and 25.9 ± 13.7. The variations in the Mann-Whitney test were 0.734 at the initial moment and 0.208 at the final moment. The variation in the comparison of the initial moment with the final moment was 0.005 providing statistical significance. For the HAM-D, the mean score went up 4 points in group 2, contrary to a 5.5 points decrease in group 1. CONCLUSION: Data analysis shows that this agent significantly improves depression, but the motor function improved only in the depressed patients. Because of the known anti-dopaminergic property of the 5-HT2c receptors, a possible approach for depression in PD could be the use of 5-HT2c antagonists, similarly to the use of atypical neuroleptics in case of psychotic symptoms.

scholarly journals LINK OF MOMENTS BEFORE AND AFTER TRANSFORMATIONS, WITH AN APPLICATION TO RESAMPLING FROM FAT-TAILED DISTRIBUTIONS

2018 ◽  
Vol 35 (03) ◽  
pp. 630-652 ◽  
Author(s):  
Karim M. Abadir ◽  
Adriana Cornea-Madeira
Keyword(s):  
Finite Number ◽  
Confidence Intervals ◽  
Characteristic Functions ◽  
Infinite Variance ◽  
Fundamental Relation ◽  
Bootstrap Confidence Intervals ◽  
Finite Samples ◽  
Before And After ◽  
The Mean ◽  
Do So

Let x be a transformation of y, whose distribution is unknown. We derive an expansion formulating the expectations of x in terms of the expectations of y. Apart from the intrinsic interest in such a fundamental relation, our results can be applied to calculating E(x) by the low-order moments of a transformation which can be chosen to give a good approximation for E(x). To do so, we generalize the approach of bounding the terms in expansions of characteristic functions, and use our result to derive an explicit and accurate bound for the remainder when a finite number of terms is taken. We illustrate one of the implications of our method by providing accurate naive bootstrap confidence intervals for the mean of any fat-tailed distribution with an infinite variance, in which case currently available bootstrap methods are asymptotically invalid or unreliable in finite samples.

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