| Sunset over Brownistan |
88 |
16 pages |
| Authors:
Erhan Cinlar; PRINCETON UNIV NJ PROGRAM IN STATISTICS AND OPERATIONS RESEARCH
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 | Consider a Brownian motion with a downward drift of rate a. Its maximum over all time has the exponential distribution with parameter 2a. Our aim is to study this maximum as a stochastic process indexed by a. That process is related to the convex majorant of the standard Brownian motion and, through the latter, to a Poisson random measure. This connection is exploited to obtain various distributional results. The results ... |
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| On Lifetimes Influenced by a Common Environment |
87 |
23 pages |
| Authors:
Erhan Cinlar; Moshe Shaked; J. G. Shanthikumar; PRINCETON UNIV NJ
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| Consider the lifelengths T sub 1,...., T sub k of k components subjected to a randomly varying environment. They are dependent on each other because of their common dependence on the environment. The parameters of the model are the distribution of the random process which describes the environment and a set of rate functions which determine the probability law of T sub 1,..., T sub k as a function of ... |
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| Random Circles and Fields on Circles |
MAY 86 |
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| Authors:
Erhan Cinlar; J. G. Wang; NORTHWESTERN UNIV EVANSTON IL
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 | The aim is to describe the exact shapes of objects that were meant to be circles or cylinders. The shapes are modeled as random fields whose parameter spaces are the intended shapes. A specific random fields on a true circle is introduced via exponential smoothing of a random noise, on the circle, with stationary and independent increments. The result is a stationary stochastically continuous random field. When the noise is ... |
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| Markov Processes Applied to Control, Replacement, and Signal Analysis |
OCT 85 |
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| Authors:
Erhan Cinlar; NORTHWESTERN UNIV EVANSTON IL
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| The concept of intrinsic age was introduced to relate the deterioration of a component under field conditions to the deterioration it would have experienced under laboratory conditions. Work has begun on research into random shapes. Additional research was performed on the stability of a harmonic oscillator in the presence of small noise. Keywords include: Intrinsic age; Random shapes; and Optimal replacement. |
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| Markov Processes Applied to Control, Replacement, and Signal Analysis |
JUL 1982 |
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| Authors:
Erhan Cinlar; NORTHWESTERN UNIV EVANSTON IL DEPT OF APPLIED MATHEMATICS
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| This report describes the work completed under the grant in the following areas: Hunt processes; queues with random intensities; martingales, Brownian motion, stochastic integrals; stochastic means; inverse problems; Brownian motion and Riemannian geometry; mean exit time from geodesics; and seminar on stochastic processes 1982. Also included are a list of the participants in the seminar; a list of contributors and the titles of their work to the proceedings of the ... |
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| Markow Processes Applied to Control, Replacement, and Signal Analysis |
MAY 80 |
5 pages |
| Authors:
Erhan Cinlar; NORTHWESTERN UNIV EVANSTON IL DEPT OF APPLIED MATHEMATICS
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| On regenerative systems and Markov additive processes, the completed work has been reported. MAISONNEUVE shows how to use the theory of regenerative systems in order to study increasing Levy processes. Levy processes as well- known objects in probability, and their probabilistic laws as well as their stochastic structures have been known for some time. Hence, when working on strictly regenerative systems, it used to be advantageous to first characterize the ... |
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| Optimal Operating Policy for the Machine Repair Problem with Two Service Stations. |
OCT 1972 |
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| Authors:
Erhan Cinlar; CONTROL ANALYSIS CORP PALO ALTO CALIF
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| Consider a system consisting of m machines operating simultaneously; suppose there are n spare machines, and suppose there are two repair stations having (s sub 1) and (s sub 2) servers respectively. When a machine fails, a spare machine (if available), is put into operation, and one of the two repair stations is chosen to repair the failed machine. The repair time of a machine is a random variable whose ... |
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| Markov Renewal Processes: Approach to Infinity. |
JUN 1972 |
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| Authors:
Erhan Cinlar; STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH
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| Considering a Markov renewal process (X sub n, T sub n) the authors is interested in the possibility of the (T sub n) having finite accumulation points. This can happen only if the underlying Markov chain ((X sub n)) goes to 'infinity'. The study is a generalization of the problem of first passage to infinity in a Markov process. Analytically, this is a generalization of the problem of uniqueness of ... |
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| Markov Renewal Processes: Regeneration Property and the Classification of States. |
MAY 1972 |
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| Authors:
Erhan Cinlar; STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH
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| The paper is a sequel to 'Markov renewal processes: Preliminaries.' Stopping times are introduced, the strong Markov property at such times is shown to hold, and certain particular applications are discussed. A classification of states is introduced, recurrence and transience and periodicity are related to the corresponding concepts for Markov chains and renewal processes, and a complete solution is provided for each problem. (Author) |
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| Markov Renewal Processes: Preliminaries. |
MAY 1972 |
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| Authors:
Erhan Cinlar; STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH
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| A Local Time for a Storage Process. |
APR 1972 |
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| Authors:
Erhan Cinlar; STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH
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| A storage system subject to a general release rule and an additive input process is considered. If (X sub t) is the content at time t, then the set X = X sub t; t> or = 0) is a standard Markov process, and the concern is the local time at x = 0 of this process X. Depending on the parameters of the system, namely the release rule and ... |
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| Periodicity in Markov Renewal Theory. |
28 JAN 1972 |
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| Authors:
Erhan Cinlar; STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH
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| In an irreducible Markov renewal process either all states are periodic or none are. In the former case they all have the same period. Periodicity and the period can be determined by direct inspection from the semi-Markov kernel defining the process. The periodicity considerably increases the complexity of the limits in Markov renewal theory especially for transient initial states. Two Markov renewal limit theorems are given with particular attention to ... |
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Reports by Author
