A thinning result for pure jump processes |
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Authors: | Fred Böker |
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Affiliation: | Institut für Statistik und Ökonometrie der Universität Göttingen, Nikolausberger Weg 9c, D-3400 Göttingen, W. Germany |
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Abstract: | A standard thinning procedure for point processes is extended to processes of pure jump type in which each jump is retained with probability p or deleted with probability 1 ? p, independently of everything else.Two theorems are proved, the first gives a sufficient condition for the existence of thinned pure jump processes, the second concerns the convergence of such processes to pure jump processes whose increments are generated by a Cox process. Some generalizations are discussed. |
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