scholarly journals Convergence to infinitely divisible distributions with finite variance for some weakly dependent sequences

2005 ◽  
Vol 9 ◽  
pp. 38-73 ◽  
Author(s):  
Jérôme Dedecker ◽  
Sana Louhichi
Keyword(s):  
Finite Variance ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible ◽  
Weakly Dependent Sequences ◽  
Weakly Dependent

On fractional linear bounds for probability generating functions

1986 ◽  
Vol 23 (4) ◽  
pp. 904-913 ◽  
Author(s):  
Claude Lefevre ◽  
Marc Hallin ◽  
Prakash Narayan
Keyword(s):  
Lower Bounds ◽  
Generating Functions ◽  
Probability Generating Function ◽  
Linear Functions ◽  
Upper And Lower Bounds ◽  
Finite Variance ◽  
Infinitely Divisible Distributions ◽  
Slight Improvement ◽  
Infinitely Divisible ◽  
The Family

The best upper and lower bounds for any probability generating function with mean m and finite variance are derived within the family of fractional linear functions with mean m. These are often intractable and simpler bounds, more useful for practical purposes, are then constructed. Direct applications in branching and epidemic theories are briefly presented; a slight improvement of the bounds is obtained for infinitely divisible distributions.

On fractional linear bounds for probability generating functions

1986 ◽  
Vol 23 (04) ◽  
pp. 904-913 ◽  
Author(s):  
Claude Lefevre ◽  
Marc Hallin ◽  
Prakash Narayan
Keyword(s):  
Lower Bounds ◽  
Generating Functions ◽  
Probability Generating Function ◽  
Linear Functions ◽  
Upper And Lower Bounds ◽  
Finite Variance ◽  
Infinitely Divisible Distributions ◽  
Slight Improvement ◽  
Infinitely Divisible ◽  
The Family

The best upper and lower bounds for any probability generating function with mean m and finite variance are derived within the family of fractional linear functions with mean m. These are often intractable and simpler bounds, more useful for practical purposes, are then constructed. Direct applications in branching and epidemic theories are briefly presented; a slight improvement of the bounds is obtained for infinitely divisible distributions.

On fractional linear bounds for probability generating functions

1986 ◽  
Vol 23 (04) ◽  
pp. 904-913
Author(s):  
Claude Lefevre ◽  
Marc Hallin ◽  
Prakash Narayan
Keyword(s):  
Lower Bounds ◽  
Generating Functions ◽  
Probability Generating Function ◽  
Linear Functions ◽  
Upper And Lower Bounds ◽  
Finite Variance ◽  
Infinitely Divisible Distributions ◽  
Slight Improvement ◽  
Infinitely Divisible ◽  
The Family

The best upper and lower bounds for any probability generating function with meanmand finite variance are derived within the family of fractional linear functions with meanm. These are often intractable and simpler bounds, more useful for practical purposes, are then constructed. Direct applications in branching and epidemic theories are briefly presented; a slight improvement of the bounds is obtained for infinitely divisible distributions.

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.

scholarly journals Distributions with complete monotone derivative and geometric infinite divisibility

1990 ◽  
Vol 22 (3) ◽  
pp. 751-754 ◽  
Author(s):  
R. N. Pillai ◽  
E. Sandhya
Keyword(s):  
Infinite Divisibility ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible ◽  
Proper Subclass ◽  
Geometric Infinite Divisibility

It is shown that a distribution with complete monotone derivative is geometrically infinitely divisible and that the class of distributions with complete monotone derivative is a proper subclass of the class of geometrically infinitely divisible distributions.

Sign in / Sign up

Export Citation Format

Share Document