Multivariate infinitely divisible distributions with the gaussian second order conditional structure

1993 ◽  
pp. 180-183 ◽  
Author(s):  
Jacek Wesolowski
Keyword(s):  
Second Order ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible

Infinitely divisible approximations for discrete nonlattice variables

2003 ◽  
Vol 35 (04) ◽  
pp. 982-1006
Author(s):  
V. Čekanavičius
Keyword(s):  
Asymptotic Expansions ◽  
Random Variables ◽  
Second Order ◽  
Independent Random Variables ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible ◽  
Compound Poisson ◽  
Set Of Points ◽  
Poisson Measures

Sums of independent random variables concentrated on discrete, not necessarily lattice, set of points are approximated by infinitely divisible distributions and signed compound Poisson measures. A version of Kolmogorov's first uniform theorem is proved. Second-order asymptotic expansions are constructed for distributions with pseudo-lattice supports.

Infinitely divisible approximations for discrete nonlattice variables

2003 ◽  
Vol 35 (4) ◽  
pp. 982-1006 ◽  
Author(s):  
V. Čekanavičius
Keyword(s):  
Asymptotic Expansions ◽  
Random Variables ◽  
Second Order ◽  
Independent Random Variables ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible ◽  
Compound Poisson ◽  
Set Of Points ◽  
Poisson Measures

Sums of independent random variables concentrated on discrete, not necessarily lattice, set of points are approximated by infinitely divisible distributions and signed compound Poisson measures. A version of Kolmogorov's first uniform theorem is proved. Second-order asymptotic expansions are constructed for distributions with pseudo-lattice supports.

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.

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