Infinitely divisible processes with interchangeable increments and random measures under convolution

1975 ◽  
Vol 32 (4) ◽  
pp. 309-321 ◽  
Author(s):  
Olav Kallenberg
Keyword(s):  
Random Measures ◽  
Infinitely Divisible ◽  
Infinitely Divisible Processes

Rarefactions of compound point processes

1984 ◽  
Vol 21 (04) ◽  
pp. 710-719
Author(s):  
Richard F. Serfozo
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Classical Result ◽  
Point Processes ◽  
Rare Events ◽  
Random Measure ◽  
Bernoulli Trials ◽  
Random Measures ◽  
Infinitely Divisible ◽  
Independent Increments

The Poisson process is regarded as a point process of rare events because of the classical result that the number of successes in a sequence of Bernoulli trials is asymptotically Poisson as the probability of a success tends to 0. It is shown that this rareness property of the Poisson process is characteristic of any infinitely divisible point process or random measure with independent increments. These processes and measures arise as limits of certain rarefactions of compound point processes: purely atomic random measures with uniformly null atom sizes. Examples include thinnings and partitions of point processes.

scholarly journals Infinite non-linear programming

1963 ◽  
Vol 3 (3) ◽  
pp. 294-300 ◽  
Author(s):  
M. A. Hanson
Keyword(s):  
Linear Programming ◽  
Mathematical Programming ◽  
Calculus Of Variations ◽  
Continuous Variable ◽  
Infinitely Divisible ◽  
Non Linear Programming ◽  
Non Linear ◽  
Mathematical Reason ◽  
Finite Spaces ◽  
Infinitely Divisible Processes

In recent years there has been extensive development in the theory and techniques of mathematical programming in finite spaces. It would be very useful in practice to extend this development to infinite spaces, in order to treat more realistically the problems that arise for example in economic situations involving infinitely divisible processes, and in particular problems involving time as a continuous variable. A more mathematical reason for seeking such generalisation is possibly that of obtaining a unification mathematical programming with other branches of mathematics concerned with extrema, such as the calculus of variations.

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