Search

We study the properties of sums of lower records from a distribution on [0,∞) which is either continuous, except possibly at the origin, or has support contained in the set of nonnegative integers. We find a necessary and sufficient condition for the partial sums of lower records to converge almost surely to a proper random variable. An explicit formula for the Laplace transform of the limit is derived. This limit is infinitely divisible and we show that all infinitely divisible random variables with continuous Lévy measure on [0,∞) originate as infinite sums of lower records.

A general method based on a limit theorem for generation of random numbers from infinitely divisible distributions with essentially given Lévy measure is studied. Some classes of infinitely divisible distributions that appear in a natural way in this context are paid particular attention.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

Convergence of lower records and infinite divisibility

On simulation from infinitely divisible distributions

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

Convergence of lower records and infinite divisibility

On simulation from infinitely divisible distributions