Geodesic
Limit behaviour of a compound Poisson process with switching between multiple values
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 44-62

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The paper deals with the limit behaviour of a compound Poisson process with switching between a finite number of sequences of i.i.d. random variables. The switching is provided with Bernulli's random variables. Under suitable normalization the limit process is a Brownian motion with switching variance. 
@article{ZNSL_2019_486_a2,
     author = {A. N. Borodin},
     title = {Limit behaviour of a compound {Poisson} process with switching between multiple values},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {44--62},
     publisher = {mathdoc},
     volume = {486},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a2/}
}
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A. N. Borodin. Limit behaviour of a compound Poisson process with switching between multiple values. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 44-62. http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a2/