Artículos de revistas
Perfect Simulation Of A Coupling Achieving The D̄-distance Between Ordered Pairs Of Binary Chains Of Infinite Order
Registro en:
Journal Of Statistical Physics. , v. 141, n. 4, p. 669 - 682, 2010.
224715
10.1007/s10955-010-0071-0
2-s2.0-78049376628
Autor
Galves A.
Garcia N.L.
Prieur C.
Institución
Resumen
We explicitly construct a stationary coupling attaining Ornstein's d̄-distance between ordered pairs of binary chains of infinite order. Our main tool is a representation of the transition probabilities of the coupled bivariate chain of infinite order as a countable mixture of Markov transition probabilities of increasing order. Under suitable conditions on the loss of memory of the chains, this representation implies that the coupled chain can be represented as a concatenation of i.i.d. sequences of bivariate finite random strings of symbols. The perfect simulation algorithm is based on the fact that we can identify the first regeneration point to the left of the origin almost surely. © 2010 Springer Science+Business Media, LLC. 141 4 669 682 Berbee, H., Chains with infinite connections: uniqueness and Markov representation (1987) Probab. Theory Relat. Fields, 76 (2), pp. 243-253 Comets, F., Fernández, R., Ferrari, P.A., Processes with long memory: regenerative construction and perfect simulation (2002) Ann. Appl. Probab., 12 (3), pp. 921-943 Ellis, M.H., The d̄-distance between two Markov processes cannot always be attained by a Markov joining (1976) Isr. J. Math., 24 (3-4), pp. 269-273 Ellis, M.H., Distances between two-state Markov processes attainable by Markov joinings (1978) Trans. Am. Math. Soc., 241, pp. 129-153 Ellis, M.H., Conditions for attaining d̄ by a Markovian joining (1980) Ann. Probab., 8 (3), pp. 431-440 Ellis, M.H., On Kamae's conjecture concerning the d̄-distance between two-state Markov processes (1980) Ann. Probab., 8 (2), pp. 372-376 Fernández, R., Ferrari, P.A., Galves, A., Coupling, renewal and perfect simulation of chains of infinite order (2001), http://www.ime.usp.br/~pablo/abstracts/vebp.html, Notes for a mini-course presented in Vth Brazilian School of Probability, 2001. Can be downloaded fromFerrari, P.A., Maass, A., Martinez, S., Ney, P., Cesàro mean distribution of group automata starting from measures with summable decay (2000) Ergod. Theory Dyn. Syst., 20 (6), pp. 1657-1670 Harris, T.E., On chains of infinite order (1955) Pac. J. Math., 5, pp. 707-724 Holley, R., Remarks on the FKG inequalities (1974) Commun. Math. Phys., 36, pp. 227-231 Iosifescu, M., Grigorescu, S., (1990) Dependence with Complete Connections and Its Applications, , Cambridge: Cambridge University Press Kalikow, S., Random Markov processes and uniform martingales (1990) Isr. J. Math., 71 (1), pp. 33-54 Kirillov, A.B., Radulescu, D.C., Styer, D.F., Vasserstein distances in two-states systems (1989) J. Stat. Phys., 56 (5-6), pp. 931-937 Lalley, S.P., Regenerative representation for one-dimensional Gibbs states (1986) Ann. Probab., 14 (4), pp. 1262-1271 Lalley, S.P., Regeneration in one-dimensional Gibbs states and chains with complete connections (2000) Resenhas, 4 (3), pp. 249-281 Lindvall, T., (1992) Lectures on the Coupling Method, , New York: Wiley Ornstein, D., An application of ergodic theory to probability theory (1973) Ann. Probab., 1 (1), pp. 43-65 Onicescu, O., Mihoc, G., Sur les chaînes statistiques (1935) C. R. Acad. Sci. Paris, 200, pp. 511-512 Rachev, S.T., The Monge-Kantorovich problem on mass transfer and its applications in stochastics (1984) Teor. Veroyatn. Primen., 29 (4), pp. 625-653. , (Russian). English translation: Theory Probab. Appl. 29(4), 647-676 Villani, C., (2009) Optimal Transport. Old and New, 338. , Grundlehren der Mathematischen Wissenschaften[Fundamental Principles of Mathematical Sciences], Berlin: Springer