Limit theorems for sums of independent random variables defined on a nonrecurrent random walk

1982 ◽  
Vol 20 (3) ◽  
pp. 2130-2137
Author(s):  
A. N. Borodin
Keyword(s):  
Random Walk ◽  
Limit Theorems ◽  
Random Variables ◽  
Independent Random Variables

A note on passage times and infinitely divisible distributions

1967 ◽  
Vol 4 (2) ◽  
pp. 402-405 ◽  
Author(s):  
H. D. Miller
Keyword(s):  
Random Walk ◽  
Markov Process ◽  
Continuous Time ◽  
Random Variables ◽  
Independent Random Variables ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible ◽  
Time Intervals ◽  
Mutually Independent ◽  
Passage Times

Let X(t) be the position at time t of a particle undergoing a simple symmetrical random walk in continuous time, i.e. the particle starts at the origin at time t = 0 and at times T1, T1 + T2, … it undergoes jumps ξ1, ξ2, …, where the time intervals T1, T2, … between successive jumps are mutually independent random variables each following the exponential density e–t while the jumps, which are independent of the τi, are mutually independent random variables with the distribution . The process X(t) is clearly a Markov process whose state space is the set of all integers.

Limit theorems for nonnegative independent random variables with truncation

2014 ◽  
Vol 145 (1) ◽  
pp. 1-16 ◽  
Author(s):  
T. Nakata
Keyword(s):  
Limit Theorems ◽  
Random Variables ◽  
Independent Random Variables
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