caa a22 4500 605463700 CHVBK 20210128100254.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s10687-014-0200-2 doi (NATIONALLICENCE)springer-10.1007/s10687-014-0200-2 Rice formula for processes with jumps and applications [Elektronische Daten] [Federico Dalmao, Ernesto Mordecki] We extend Rice Formula to a process which is the sum of two independent processes: a smooth process and a pure jump process with finitely many jumps. Formulas for the mean number of both continuous and discontinuous crossings through a fixed level on a compact time interval are obtained. We present examples in which we compute explicitly the mean number of crossings and compare which kind of crossings dominates for high levels. In one of the examples the leading term of the tail of the distribution function of the maximum of the process over a compact time interval as the level goes to infinity is obtained. We end giving a generalization, to the non-stationary case, of Borovkov-Last's Rice Formula for Piecewise Deterministic Markov Processes. Springer Science+Business Media New York, 2014 Rice formula nationallicence Level crossings nationallicence Process with jumps nationallicence Number of continuous and discontinuous crossings nationallicence Dalmao Federico Departamento de Matemática y Estadística del Litoral, Regional Norte, Universidad de la República, Rivera 1350, 50000, Salto, Uruguay aut Mordecki Ernesto Centro de Matemática, Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400, Montevideo, Uruguay aut Extremes Springer US; http://www.springer-ny.com 18/1(2015-03-01), 15-35 1386-1999 18:1<15 2015 18 10687 https://doi.org/10.1007/s10687-014-0200-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10687-014-0200-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dalmao Federico Departamento de Matemática y Estadística del Litoral, Regional Norte, Universidad de la República, Rivera 1350, 50000, Salto, Uruguay aut NATIONALLICENCE 700 1- Mordecki Ernesto Centro de Matemática, Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400, Montevideo, Uruguay aut NATIONALLICENCE 773 0- Extremes Springer US; http://www.springer-ny.com 18/1(2015-03-01), 15-35 1386-1999 18:1<15 2015 18 10687