Weak convergence of random walks conditioned to stay away

@article{PajorGyulai2010WeakCO,
title={Weak convergence of random walks conditioned to stay away},
author={Zsolt Pajor-Gyulai and Domokos Sz'asz},
journal={arXiv: Probability},
year={2010}
}
• Published 3 September 2010
• Mathematics
• arXiv: Probability
Let $\{X_n\}_{n\in\mathbb{N}}$ be a sequence of i.i.d. random variables in $\mathbb{Z}^d$. Let $S_k=X_1+...+X_k$ and $Y_n(t)$ be the continuous process on $[0,1]$ for which $Y_n(k/n)=S_k/\sqrt{n}$ $k=1,...,n$ and which is linearly interpolated elsewhere. The paper gives a generalization of results of Belkin, \cite{B72} on the weak limit laws of $Y_n(t)$ conditioned to stay away from some small sets. In particular, it is shown that the diffusive limit of the random walk meander on \$\mathbb Z^d…
1 Citations
Energy Transfer and Joint Diffusion
• Physics, Mathematics
• 2010
A paradigm model is suggested for describing the diffusive limit of trajectories of two Lorentz disks moving in a finite horizon periodic configuration of smooth, strictly convex scatterers and

References

SHOWING 1-10 OF 14 REFERENCES
On a Functional Central Limit Theorem for Random Walks Conditioned to Stay Positive
: Let { X k : k ≧ 1 } be a sequence of i.i.d.rv with E ( X i ) = 0 and E ( X 2 i ) = σ 2 , 0 < σ 2 < ∞ . Set S n = X 1 + · · · + X n . Let Y n ( t ) be S k /σn 1 2 for t = k/n and suitably
Weak convergence of probability measures and random functions in the function space D[0,∞)
• T. Lindvall
• Mathematics
Journal of Applied Probability
• 1973
This paper extends the theory of weak convergence of probability measures and random functions in the function space D[0,1] to the case D [0,∞), elaborating ideas of C. Stone and W. Whitt. 7)[0,∞) is
Convergence of Probability Measures
Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.
Energy Transfer and Joint Diffusion
• Physics, Mathematics
• 2010
A paradigm model is suggested for describing the diffusive limit of trajectories of two Lorentz disks moving in a finite horizon periodic configuration of smooth, strictly convex scatterers and
Szász. Energy Transfer and Joint diffusion, submitted to Communications in Mathematical Physics
• Szász. Energy Transfer and Joint diffusion, submitted to Communications in Mathematical Physics
Belkin A limit theorem for conditioned recurrent random walk attracted to a stable law The Annals of Mathematical Statistics
• Belkin A limit theorem for conditioned recurrent random walk attracted to a stable law The Annals of Mathematical Statistics
• 1970
Bolthausen On a functional central limit theorem for random walks conditioned to stay positive The Annals of Probability
• Bolthausen On a functional central limit theorem for random walks conditioned to stay positive The Annals of Probability
• 1976