Geodesic
Distributions of functionals of diffusions with jumps connected with the location of the maximum or minimum
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 16, Tome 384 (2010), pp. 78-104 
A. N. Borodin. Distributions of functionals of diffusions with jumps connected with the location of the maximum or minimum. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 16, Tome 384 (2010), pp. 78-104. http://geodesic.mathdoc.fr/item/ZNSL_2010_384_a4/
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     title = {Distributions of functionals of diffusions with jumps connected with the location of the maximum or minimum},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_384_a4/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper deals with methods of computations of distributions of integral functionals of diffusions with jumps at the time moments, in which the maximum and the minimum values of diffusions are achieved. As an example an explicit formulas for the Laplace transform of joint locations of minimum and maximum of the process equal the sum of Brownian motion and the compound Poisson process are obtained. Bibl. 7 titles.

[1] A. N. Borodin, “Raspredeleniya momentov dostizheniya minimumov i maksimumov dlya skachkoobraznykh diffuzii”, Zap. nauchn. semin. POMI, 368, 2009, 75–94

[2] E. Csáki, A. Földes, P. Salminen, “On the joint distribution of the maximum and its location for a linear diffusion”, Ann I. H. P., 23:2 (1987), 179–194 | MR | Zbl

[3] A. N. Borodin, “Raspredelenie funktsionalov ot skachkoobraznykh diffuzii”, Zap. nauchn. semin. POMI, 339, 2006, 15–36 | MR | Zbl

[4] A. N. Borodin, “Raspredelenie funktsionalov ot mostov skachkoobraznykh diffuzii”, Zap. nauchn. semin. POMI, 341, 2007, 34–47 | MR | Zbl

[5] A. N. Borodin, “O momente pervogo vykhoda iz intervala dlya diffuzii so skachkami”, Zap. nauchn. semin. POMI, 364, 2009, 70–87 | Zbl

[6] E. Mordecki, “Ruin probabilities for Lévy processes with mixed exponential negative jumps”, Theory Probab. Appl., 48:1 (2003), 188–194 | MR | Zbl

[7] A. N. Borodin, “Raspredelenie funktsionalov ot nekotorykh protsessov s nezavisimymi prirascheniyami”, Vestnik SPbGU, Ser. 1, 2005, no. 4, 7–20 | MR | Zbl