Abstract
A new construction of mixed Poisson processes with prescribed distributions for their claim interarrival times is given. As a consequence, some concrete examples of constructing such processes useful for applications are presented and the corresponding disintegrating and claim measures are computed.
[1] FADEN, A. M.: The existence of regular conditional probabilities: Necessary and sufficient conditions, Ann. Probab. 13 (1985), 288–298. http://dx.doi.org/10.1214/aop/117699308110.1214/aop/1176993081Search in Google Scholar
[2] FREMLIN, D. H.: Measure Theory, Vol. 1. The Irreducible Minimum, Torres Fremlin, Colchester, 2000. Search in Google Scholar
[3] FREMLIN, D. H.: Measure Theory, Vol. 4. Topological measure spaces. Part I, II, Torres Fremlin, Colchester, 2003. Search in Google Scholar
[4] GRANDELL, J.: Mixed Poisson Processes, Chapman & Hall, London, 1997. 10.1007/978-1-4899-3117-7Search in Google Scholar
[5] LYBEROPOULOS, D. P.— MACHERAS, N. D.: Some characterizations of mixed Poisson processes, Sankhyā Ser. A (2012), doi: 10.1007/s13171-012-0011-y. 10.1007/s13171-012-0011-ySearch in Google Scholar
[6] PACHL, J. K.: Disintegration and compact measures, Math. Scand. 43 (1978), 157–168. 10.7146/math.scand.a-11771Search in Google Scholar
[7] RAMACHANDRAN, D.: Perfect Measures, Part I, Basic Theory, The Macmillan Company of India Limited, Delhi-Bombay-Calcutta-Madras, 1979. Search in Google Scholar
[8] SCHMIDT, K. D.: Lectures on Risk Theory, B. G. Teubner, Stuttgart, 1996. http://dx.doi.org/10.1007/978-3-322-90570-310.1007/978-3-322-90570-3Search in Google Scholar
[9] STRAUSS, W.— MACHERAS, N. D.— MUSIAL, K.: Splitting of liftings in products of probability spaces, Ann. Probab. 32 (2004), 2389–2408. http://dx.doi.org/10.1214/00911790400000001810.1214/009117904000000018Search in Google Scholar
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