Geodesic
Limit behaviour of a compound Poisson process with switching
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 54-66 
A. N. Borodin. Limit behaviour of a compound Poisson process with switching. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 54-66. http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a3/
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     author = {A. N. Borodin},
     title = {Limit behaviour of a compound {Poisson} process with switching},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {54--66},
     year = {2017},
     volume = {466},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a3/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper deals with the limit behaviour of a compound Poisson process with switching. The switching is provided with Bernulli's random variables. Under suitable normalization the limit process is a Brownian motion with switching variance.

[1] A. N. Borodin, Sluchainye protsessy, Lan, Sankt-Peterburg, 2013

[2] A. N. Borodin, “Raspredeleniya funktsionalov ot telegrafnogo protsessa i diffuzii s pereklyucheniyami”, Zap. nauchn. semin. POMI, 466, 2017, 38–53

[3] P. Billingsli, Skhodimost veroyatnostnykh mer, Nauka, M., 1977 | MR