View More View Less
  • 1 University of Maryland Department of Mathematics, Mathematics Building College Park MD 20742-4015 USA
  • | 2 Budapest University of Technology and Economics Department of Stochastics, Institute of Mathematics 1111 Egry J. u. 1 Budapest Hungary
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

Let {Xn}n∈ℕ be a sequence of i.i.d. random variables in ℤd. Let Sk = X1 + … + Xk and Yn(t) be the continuous process on [0, 1] for which Yn(k/n) = Sk/n1/2 for k = 1, … n and which is linearly interpolated elsewhere. The paper gives a generalization of results of ([2]) on the weak limit laws of Yn(t) conditioned to stay away from some small sets. In particular, it is shown that the diffusive limit of the random walk meander on ℤd: d ≧ 2 is the Brownian motion.

  • Belkin, B., A limit theorem for conditioned recurrent random walk attracted to a stable law, The Annals of Mathematical Statistics, 41, No. 1, 146–163, 1970.

    Belkin B. , 'A limit theorem for conditioned recurrent random walk attracted to a stable law ' (1970 ) 41 The Annals of Mathematical Statistics : 146 -163.

    • Search Google Scholar
  • Belkin, B., An invariance principle for conditioned recurrent random walk attracted to a stable law, Probability Theory and Related Fields, 21, No. 1, 45–64, 1972.

    Belkin B. , 'An invariance principle for conditioned recurrent random walk attracted to a stable law ' (1972 ) 21 Probability Theory and Related Fields : 45 -64.

    • Search Google Scholar
  • Billingsley, P., Convergence of probability measures, Wiley, New York, 1968

    Billingsley P. , '', in Convergence of probability measures , (1968 ) -.

  • Bolthausen, E., On a functional central limit theorem for random walks conditioned to stay positive, The Annals of Probability, 4, No. 3, 480–485, 1976.

    Bolthausen E. , 'On a functional central limit theorem for random walks conditioned to stay positive ' (1976 ) 4 The Annals of Probability : 480 -485.

    • Search Google Scholar
  • Lindvall, T., Weak Convergence of Probability Measures and Random Functions in the Function Space D[0, ∞), Journal of Applied Probability, 10, No. 1, 109–121, 1973.

    Lindvall T. , 'Weak Convergence of Probability Measures and Random Functions in the Function Space D[0, ∞) ' (1973 ) 10 Journal of Applied Probability : 109 -121.

    • Search Google Scholar
  • Pajor-Gyulai, Zs. and Szász, D., Energy Transfer and Joint diffusion, Proc. XVIth International Congress on Mathematical Physics. ed. P. Exner. World Scientific, 328–332, 2010.

  • Pajor-Gyulai, Zs. and Szász, D., Energy Transfer and Joint diffusion, to appear in Journal of Statistical Physics, 146 (2012), no. 5, 1001–1025.

    Szász D. , 'Energy Transfer and Joint diffusion ' (2012 ) 146 Journal of Statistical Physics : 1001 -1025.

    • Search Google Scholar
  • Whitt, W., Weak Convergence of Probability Measures on the Function Space C[0, ∞), The Annals of Mathematical Statistics, 41, No. 3, 939–944, 1970.

    Whitt W. , 'Weak Convergence of Probability Measures on the Function Space C[0, ∞) ' (1970 ) 41 The Annals of Mathematical Statistics : 939 -944.

    • Search Google Scholar