A large deviations principle (LDP), demonstrated for occupancy
problems with indistinguishable balls, is generalized to the case
in which balls are distinguished by a finite number of colors. The
colors of the balls are chosen independently from the occupancy
process itself. There are r balls thrown into n urns
with the probability of a ball entering a given urn being
1/n (i.e. Maxwell-Boltzmann statistics). The LDP applies
with the scale parameter, n, tending to infinity and
r increasing proportionally. The LDP holds under mild
restrictions, the key one being that the coloring process by
itself satisfies an LDP. This includes the important special cases
of deterministic coloring patterns and colors chosen with fixed
probabilities independently for each ball.
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References
Bailey, N. T. J. (1951). On estimating the size of mobile populations from recapture data. Biometrika 38, 293--306.
Boucheron, S., Gamboa, F. and Leonard C. (2002). Bins and balls: large deviations of the empirical occupancy process. Ann. Appl. Prob. 2, 1--30.
Chao, A. (2001). An overview of closed capture--recapture models. J. Agricultural Biol. Environ. Statist. 6, 158--175.
Dupuis, P. and Ellis, R. S. (1997). A Weak Convergence Approach to Large Deviations. John Wiley, New York.
Dupuis, P., Ellis, R. S. and Weiss, A. (1991). Large deviations for Markov processes with discontinuous statistics. I. General upper bounds. Ann. Prob. 19, 1280--1297.
Dupuis, P., Nuzman, C. and Whiting, P. (2003). Occupancy models and circuit switched networks with blocking. In Proc. 41st Annual Allerton Conf. Commun. Control Comput. (September 2003), University of Illinois Press, Champaign, IL.
Dupuis, P., Nuzman, C. and Whiting, P. (2004). Large deviation asymptotics for occupancy problems. Ann. Prob. 32, 2765--2818.
Eramo, V., Listanti, M., Nuzman, C. and Whiting, P. (2002). Optical switch dimensioning and the classical occupancy problem. Internat. J. Commun. 15, 127--141.
Finkelstein, M., Tucker, H. G. and Veeh, J. A. (1998). Confidence intervals for the number of unseen types. Statist. Prob. Lett. 37, 423--430.
Graham, C. and O'Connell, N. (2002). Large deviations at equilibrium for a large star-shaped loss network. Ann. Appl. Prob. 2, 1807--1856.
Johnson, N. L. and Kotz, S. (1977). Urn Models and Their Application. John Wiley, New York.
Mathematical Reviews (MathSciNet):
MR488211
Kelly, F. P. and Ziedins, I. (1989). Blocking in star networks. Adv. Appl. Prob. 21, 804--830.
Kotz, S. and Balakrishnan, N. (1997). Advances in urn models during the past two decades. In Advances in Combinatorial Methods and Applications to Probability and Statistics, ed. N. Balakrishnan, Birkhäuser, Boston, MA, pp. 203--257.
Seber, G. A. F. (1982). The Estimation of Animal Abundance and Related Parameters, 2nd edn. Macmillan, New York.
Mathematical Reviews (MathSciNet):
MR686755
Vander Wiel, S. A. and Votta, L. G. (1993). Assessing software designs using capture-recapture methods. IEEE Trans. Software Eng. 19, 1045--1054.
Whitt, W. (1985). Blocking when service is required from several facilities simultaneously. AT&T Tech. J. 64, 1807--1856.
Mathematical Reviews (MathSciNet):
MR812939
