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RESEARCH PRODUCT
Hitting straight lines by compound Poisson process paths
Hans-j. SchuhWolfgang J. BühlerPrem S. Purisubject
Statistics and ProbabilityLaplace transformDifferential equationMathematical analysisProbabilistic logicPoisson processParallelGalton–Watson processCombinatoricssymbols.namesakeIntersectionCompound Poisson processsymbolsMathematicsdescription
In a recent article Mallows and Nair (1989,Ann. Inst. Statist. Math.,41, 1–8) determined the probability of intersectionP{X(t)=αt for somet≥0} between a compound Poisson process {X(t), t≥0} and a straight line through the origin. Using four different approaches (direct probabilistic, via differential equations and via Laplace transforms) we extend their results to obtain the probability of intersection between {X(t), t≥0} and arbitrary lines. Also, we display a relationship with the theory of Galton-Watson processes. Additional results concern the intersections with two (or more) parallel lines.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1990-12-01 | Annals of the Institute of Statistical Mathematics |