Estimates of the remainder term in limit theorems in the case of stable limit law

1974 ◽  
Vol 14 (1) ◽  
pp. 127-146 ◽  
Author(s):  
V. I. Paulauskas
Keyword(s):  
Remainder Term ◽  
Limit Theorems ◽  
Stable Limit

A central limit theorem by remainder term for renewal processes

1992 ◽  
Vol 24 (2) ◽  
pp. 267-287 ◽  
Author(s):  
Allen L. Roginsky
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Renewal Processes

Three different definitions of the renewal processes are considered. For each of them, a central limit theorem with a remainder term is proved. The random variables that form the renewal processes are independent but not necessarily identically distributed and do not have to be positive. The results obtained in this paper improve and extend the central limit theorems obtained by Ahmad (1981) and Niculescu and Omey (1985).

Some Functional Stable Limit Theorems

1973 ◽  
Vol 16 (2) ◽  
pp. 173-177 ◽  
Author(s):  
D. R. Beuerman
Keyword(s):  
Weak Convergence ◽  
Limit Theorems ◽  
Stable Process ◽  
Random Variables ◽  
Domain Of Attraction ◽  
Stable Processes ◽  
Stable Limit ◽  
Stable Law ◽  
Partial Sum Process ◽  
Image Position

Let Xl,X2,X3, … be a sequence of independent and identically distributed (i.i.d.) random variables which belong to the domain of attraction of a stable law of index α≠1. That is,1whereandwhere L(n) is a function of slow variation; also take S0=0, B0=l.In §2, we are concerned with the weak convergence of the partial sum process to a stable process and the question of centering for stable laws and drift for stable processes.

scholarly journals α-Stable limit theorems for sums of dependent random vectors

1989 ◽  
Vol 29 (2) ◽  
pp. 219-251 ◽  
Author(s):  
Adam Jakubowski ◽  
Maria Kobus
Keyword(s):  
Limit Theorems ◽  
Stable Limit ◽  
Random Vectors

scholarly journals Stable limit theorems for empirical processes under conditional neighborhood dependence

Bernoulli ◽  
2019 ◽  
Vol 25 (2) ◽  
pp. 1189-1224 ◽  
Author(s):  
Ji Hyung Lee ◽  
Kyungchul Song
Keyword(s):  
Limit Theorems ◽  
Empirical Processes ◽  
Stable Limit

A Central Limit Theorem for Cumulative Processes

1994 ◽  
Vol 26 (01) ◽  
pp. 104-121 ◽  
Author(s):  
Allen L. Roginsky
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Rate Of Convergence ◽  
Central Limit ◽  
Remainder Term ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Independent Random Variables ◽  
Cumulative Processes

A central limit theorem for cumulative processes was first derived by Smith (1955). No remainder term was given. We use a different approach to obtain such a term here. The rate of convergence is the same as that in the central limit theorems for sequences of independent random variables.

Sign in / Sign up

Export Citation Format

Share Document