A Functional Limit Theorem for Additively Separable Statistics in the Case of Very Rare Events

1986 ◽  
Vol 30 (3) ◽  
pp. 622-626 ◽  
Author(s):  
R. M. Mnatsakanov
Keyword(s):  
Limit Theorem ◽  
Rare Events ◽  
Functional Limit Theorem ◽  
Functional Limit

Convergence to the local time of Brownian meander

2019 ◽  
Vol 29 (3) ◽  
pp. 149-158 ◽  
Author(s):  
Valeriy. I. Afanasyev
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Local Time ◽  
Random Processes ◽  
Functional Limit Theorem ◽  
Zero Drift ◽  
Functional Limit ◽  
Brownian Meander

Abstract Let {Sn, n ≥ 0} be integer-valued random walk with zero drift and variance σ2. Let ξ(k, n) be number of t ∈ {1, …, n} such that S(t) = k. For the sequence of random processes $\begin{array}{} \xi(\lfloor u\sigma \sqrt{n}\rfloor,n) \end{array}$ considered under conditions S1 > 0, …, Sn > 0 a functional limit theorem on the convergence to the local time of Brownian meander is proved.

A conditioned functional limit theorem

1980 ◽  
Vol 12 (2) ◽  
pp. 296-297
Author(s):  
Wim Vervaat ◽  
J. C. Smit
Keyword(s):  
Limit Theorem ◽  
Functional Limit Theorem ◽  
Functional Limit
Sign in / Sign up

Export Citation Format

Share Document