Limit theorems for monotone Markov processes
Tóm tắt
Từ khóa
Tài liệu tham khảo
Bhattacharya, R.N. (1982). On the functional central limit theorem and the law of the iterated logarithm for Markov processes. Z. Wahrsch. Verw. Gebiete, 60, 185–201.
Bhattacharya, R.N. and Lee, O. (1988). Asymptotics of a class of Markov processes which are not in general irreducible. Ann. Probab., 16, 1333–1347 (correction (1997): Ann. Probab., 25, 1541–43).
Bhattacharya, R.N. and Majumdar, M. (1999). On a theorem of Dubins and Freedman. J. Theoret. Probab., 12, 1067–1087.
Bhattacharya, R.N. and Majumdar, M. (2001). On a class of random dynamical systems: theory and applications. J. Econom. Theory, 96, 208–229.
Bhattacharya, R.N. and Majumdar, M. (2004). Stability in distribution of randomly perturbed quadratic maps as Markov processes. Ann. Appl. Probab., 14, 1802–1809.
Bhattacharya, R.N. and Majumdar, M. (2007). Random Dynamical Systems: Theory and Applications. Cambridge University Press, Cambridge.
Bhattacharya, R.N. and Majumdar, M. (2010). Random iterates of monotone maps. Rev. Econ. Des., 14, 185–192.
Bhattacharya, R.N. and Ranga Rao, R. (1976). Normal Approximation and Asymptotic Expansions. John Wiley and Sons, New York.
Bhattacharya, R.N. and Rao, B.V. (1993). Random iteration of two quadratic maps. In Stochastic Processes: A Festschrift in Honour of Gopinath Kallianpur, (Cambanis, S., Ghosh, J.K., Karandikar, R.L. and Sen, P.K., eds.). Springer-Verlag, New York, 13–22.
Bhattacharya, R.N. and Waymire, E.C. (2009). Stochastic Processes with Applications. SIAM Classics in Applied Mathematics, 61. SIAM, Philadelphia.
Billingsley, P. (1968). Convergence of Probability Measures. Wiley, New York.
Blumenthal, R.M. and Corson, H. (1972). On continuous collections of measures. In Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, 2, (L.M. Le Cam, J. Neyman and E.L. Scott, eds.). Univ. California Press, Berkeley, 33–40.
Chakraborty, S. and Rao, B.V. (1998) Completeness of Bhattacharya metric on the space of probabilities. Statist. Probab. Lett., 36, 321–326.
Diaconis, P. and Freedman, D. (1966). Invariant probabilities for certain Markov processes. Ann. Math. Statist., 37, 837–868.
Ellner, S. (1984). Asymptotic behavior of some stochastic difference equation population models. J. Math. Biol., 19, 169–200.
Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. 2. Second Edition. John Wiley and Sons, New York.
Gordin, M.I. and Lifsic, B.A. (1978). The central limit theorem for stationary Markov processes (English translation). Soviet Math. Dokl., 19, 392–394.
Hopenhayn, H.A. and Prescott, E.C. (1992). Stochastic monotonicity and stationary distributions for dynamic economies. Econometrica, 60, 1387–1406.
Iams, S. and Majumdar, M. (2010). Stochastic equlibrium: concepts and computations for Lindley processes. Internat. J. of Econom. Theory, 6, 47–56.
Lindley, D.V. (1952). The theory of queues with a single server. Math. Proc. Cambridge Philos. Soc., 48, 277.
Lindvall, T. (1992). Lectures on the Coupling Method. John Wiley and Sons, New York.
Lund, R.B. and Tweedie, R.L. (1996). Geometric convergence rates for stochastically ordered Markov chains. Math. Oper. Res., 21, 182–194.
Maitra, A. (1968). Discounted dynamic programming on compact metric spaces. Sankhyā, Ser. A, 27, 241–248.
Majumdar, M. and Mitra, T. (1983). Dynamic optimization with non-convex technology: The case of a linear objective function. Rev. Econom. Stud., 50, 143–151.
Majumdar, M., Mitra, T. and Nyarko, Y. (1989). Dynamic optimization under uncertainty: non-convex feasible set. In Joan Robinson and Modern Economic Theory, (G. Feiwel et al., eds.). Macmillan, New York, 545–590.
Meyn, S.P. and Tweedie, R.L. (1993). Markov Chains and Stochastic Stability. Springer-Verlag, New York.
Ross, S.M. (1983). Introduction to Stochastic Dynamic Programming. Academic Press, New York.
Spitzer, F. (1956). A combinatorial lemma and its application to probability theory. Trans. Amer. Math. Soc., 82, 323–339.