A Functional Limit Theorem for Random Variables with Strong Residual Dependence

1996 ◽  
Vol 40 (4) ◽  
pp. 714-728
Author(s):  
O. V. Rusakov
Keyword(s):  
Limit Theorem ◽  
Random Variables ◽  
Functional Limit Theorem ◽  
Functional Limit

scholarly journals Functional Limit Theorem for Products of Sums of Independent and Nonidentically Distributed Random Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Przemysław Matuła ◽  
Iwona Stępień
Keyword(s):  
Limit Theorem ◽  
Weak Convergence ◽  
Limit Theorems ◽  
Random Variables ◽  
Functional Limit Theorem ◽  
Functional Limit ◽  
Generalize Limit ◽  
Products Of Sums

We study the weak convergence in the spaceD[0,1]of processes constructed from products of sums of independent but not necessarily identically distributed random variables. The presented results extend and generalize limit theorems known so far for i.i.d. sequences.

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
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