Modelling sequential events for risk, safety and maintenance assessments

• Autorzy: Eid M.
• Języki publikacji: EN

Abstrakty

EN

Assessing the Occurrence Probability of a given sequence of events in a determined order is necessary in many scientific fields. That is the case in the following fields: nucleation and microstructure growth in materials, Narrow-Band process, financial risk analysis, Sequential detection theory, rainfall modelling, in optics to model the sequences of photoelectrons under detection, population biology, software reliability, queuing in network traffic exhibiting long-range dependence behaviour, and DNA sequences and gene time expression modelling. However, the topic has a particular interest in the field of risk, safety and maintenance assessments. The lecture will focus on sequences composed of Double Stochastic Poisson Processes.

Słowa kluczowe

EN

probability; sequential events; double Poisson Stochastic Process; modulated; spectral; polynomial

• Wydawca: Polskie Towarzystwo Bezpieczeństwa i Niezawodności
• Czasopismo: Journal of Polish Safety and Reliability Association
• Rocznik: 2010
• Tom: Vol. 1, No. 1
• Strony: 83--88
• Opis fizyczny: Bibliogr. 24 poz., tab., wykr.

Twórcy

autor

Eid M.

• CEA/DANS DM2S SERMA, Saclay, F-91191 Gif sur Yvette Cedex, France

Bibliografia

• [1] Rios, P. R. et al. (2009). Inhomogeneous Poisson Point Process Nucleation : Comparaison of Analytical Solution with Cellular Automata Simulation. Material Research, Vol. 12, No 2, 219-224.
• [2] Bouzas, P. R. et al. (2006). On the characteristic functional of a doubly stochastic Poisson process: Application to a narrow-band process. Applied Mathematical Modelling, 30, 1021-1032.
• [3] Park, S. (2009). Analytical binomial lookback options with double-exponential jumps. Journal of the Korean Statistical Society 38, 397-404.
• [4] Casarin, R. (2005). Stochastic Processes in Credit Risk Modelling. CEREMADE, Dept. Of Mathematics, University Paris IX (Dauphine) and Dept. of Economics-University of Brescia. Lecture on March 10.
• [5] Fleisher, S. Hardish, S. & Shwedyk, E. (1988). A Generalized Two-Threshold Detection Procedure. IEEE Transactions on Information Theory. Vol. 34, No. 2.
• [6] Kailath, T. (1998). Detection of Stochastic Processes. IEEE Transactions on Information Theory, Vol. 44, No. 6.
• [7] Verdu, S. Poisson Communication Theory. The International Technion Communication Day in Honor of Israel Bar-David.
• [8] Onof, C., Yameundjeu, Paoli, J. P. & Ramesh, N. (2002). A Markov modulated Poisson process model for rainfall increments. Water Science and Technology, Vol.45 (2), 91-97.
• [9] Teich, M. C. & Saleh, B. E. A.. Processus stochastiques en cascade d'importance en optique. Cascaded stochastic processes in optics.
• [10] Wilkinson, R. D. & Tavaré, S. (2009). Estimating primate divergence times by using conditioned birth-and-death Processes. Theoretical Population Biology 75, 278-285.
• [11] Zheng, Y. & Renzuo, Xu. (2008). A Composite Stochastic Process Model for Software Reliability. 2008 International Conference on Computer Science and Software Engineering, 978-0-7695-3336-0/08. © 2008 IEEE, DOI 10.1109/CSSE.2008.1061.
• [12] Ryden, T. (1996). An EM algorithm for estimation in Markov-modulated Poisson processes. Computational Statistics & Data Analysis 21, 431447.
• [13] Salvador, P., Valadas, R. & Pacheco, A. (2003). Multiscale Fitting Procedure Using Markov Modulated Poisson Processes. Telecommunication Systems 23: 1, 2, 123-148, 2003. © 2003 Kluwer Academic Publishers. Manufactured in The Netherlands.
• [14] Artem, S. Novozhilov, G., Karev, P. & Koonin, E. V. (2006). Biological applications of the theory of birth-and-death processes. Briefings in Bioinformatics. Vol 7. Nn 1. 70-85. Published by Oxford University Press.
• [15] Lèbre, S. (2007). Analyse de processusstochastiques pour la génomique: étude du modèle MTD et inférence de réseaux bayésiensdynamiques. Thèse Docteur en Sciences , University of Evry-Val-d’Essone, France.
• [16] Karlin, S. & McGregor, J. L. (1957). The differential equations of birth-and-death processes, and the Stieltjes moment problem, Transactions of the American Mathematical Society 85, no. 2, 489-546.
• [17] Karlin, S. & McGregor, J. Coincidence Properties of Birth and Death Processes.” http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.pjm/1103038888&page=record.
• [18] Van Doorn. E. A. & Zeifman, A. I. (2005). Birthdeath processes with killing. Statistics & Probability Letters 72, 33-42.
• [19] Valent, G. (2005). From asymptotic to spectra measures: determinate versus indeterminate,moment problems. International MediterraneanCongress of Mathematics, Almeria, 6-10.
• [20] Coolen-Schrijner. (2006). Quasi-Stationary Distributions for Birth-Death Processes with Killing. J. of Applied Mathematics and Stochastic Analysis, page 1-15, article ID 84640.
• [21] Langovoy, M. ( 2007). Algebraic polynomials and moments of stochastic integrals. Imsartgeneric ver. 2007/04/13 file: Estimates_Stochastic_Integrals.tex date: October 28, 2009. EURANDOM, Technische Universiteit Eindhoven, 5600 MB Eindhoven, The Netherlands.
• [22] Peccati, G. & Taqqu, M. S. (2008), Central limit theorems for double Poisson Integrals. Bernoulli 14 (3), 791-821.
• [23] Błaszczyszyn, B. & Scott, R. (2002). Approximate decomposition of some modulated-Poisson Voronoi tessellations. Rapport INRIA, N° 4585, October, 2002.
• [24] Eid, M. (2010). Spectral Probability Function forthe modelling of Double Poisson Stochastic Processes. Journal of Risk and Reliability. Underreviewing, Feb. 2010.