Abstract
Stochastic processes have, since a long time, large applications in quite different domains. The standard theory considers discrete or continuous state space. We consider here the concept of Stochastic Process associated to all the cases of symbolic variables: quantitative, categorical single and multiple, interval, modal. More particularly, we adapt the definition of Markov Chain and give the equivalent of the Chapman-Kolmogorov theorem in all cases.
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References
AFONSO, F., BILLARD, L. and DIDAY, E. (2004): Régression linéaire symbolique avec variables taxonomiques. Revue RNTI. G. Hébrail et al. Eds., Vol. 1, 205–210, Cépadues.
BAILEY, T.J. (1964): The Elements of Stochastic Processes with Applications to the Natural Sciences. Wiley, New York.
BARTLETT, M.S. (1978): An Introduction to Stochastic Processes. Cambridge University Press, 3rd ed., Cambridge.
BEICHELT, F. (2006): Stochastic Processes in Science, Engineering and Finance. Chapman & Hall.
BOCK, H.-H., DIDAY, E. (2000): Analysis of Symbolic Data, Exploratory methods for extracting statistical information from complex data. Studies in Classification, Data Analysis and Knowledge Organisation, Springer-Verlag, Berlin.
COX, D.R. and MILLER, H.D. (1965): The Theory of Stochastic Processes. Methuen & Co., London.
DARSOW, W.F., NGUYEN, B. and OLSEN, E.T. (1992): Copulas and Markov processes. Illinois J. Math. 36, 600–642.
De CARVALHO, F.A.T., LIMA NETO, E.A. and TENÓRIO, C.P. (2004): A new method to fit a linear regression model for interval-valued data. In: S. Biundo, T. Frühwirth and G. Palm (Eds.): Advances in Artificial Intelligence: Proceedings of the Twenty seventh German Conference on Artificial Intelligence. Springer-Verlag, Berlin, 295–306.
FELLER, W. (1968): An Introduction to Probability Theory and its Applications Wiley, New York.
GIKHMAN, I.I. and SKOROKHOD, A.V. (2004): The Theory of Stochastic Processes. Classics in Mathematics. Springer-Verlag, Berlin.
JOE, H. (1997): Multivariate Models and Dependence Concepts. Chapman & Hall, London.
KARLIN, S. (1966): A First Course in Stochastic Processes. Academic Press, New York.
LAWLER, G.F. (2006): Introduction to Stochastic Processes, 2nd Ed. Chapman & Hall.
MEYN, S.P. and TWEEDIE, R.L. (1993): Markov Chains and Stochastic Stability. Communications & Control. Springer-Verlag, New York.
NELSEN, R.B. (1999): An introduction to Copulas. Lecture Notes in Statistics. Springer, New York.
NEVEU, J. (1964): Bases Mathématiques du Calcul des Probabilités. Masson, Paris.
PRABHU, N.V. (1965): Stochastic Processes. MacMillan, New York.
PRUDENCIO, R.B.C., LUDERMIR, T., and De CARVALHO, F.A.T. (2004): A modal symbolic classifier for selecting time series models. Pattern Recognition Letters, 25(8), 911–921.
SOULE, A., SLAMETIAN, K., TAFT, N. and EMILION, R. (2004): Flow classification by histograms. ACM Sigmetrics. New York, http://ps.lip6.fr/soule/SiteWeb/Publication.php.
STIRZAKER, D. (2005): Stochastic Processes and Models. Oxford University Press, Oxford.
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Noirhomme-Fraiture, M., Cuvelier, E. (2007). Symbolic Markov Chains. In: Brito, P., Cucumel, G., Bertrand, P., de Carvalho, F. (eds) Selected Contributions in Data Analysis and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73560-1_10
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DOI: https://doi.org/10.1007/978-3-540-73560-1_10
Publisher Name: Springer, Berlin, Heidelberg
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