The paper deals with limit behavior of a compound Poisson process with switching and dominated summands. The switching is provided by Bernulli’s random variables and a Markov chain. Under suitable normalization the limit process is a Brownian motion with switching variance and jumps.
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A. N. Borodin, “Limit Behavior of a Compound Poisson Process with Switching,” Zap. Nauchn. Semin. POMI, 466, 54–66 (2017).
A. N. Borodin, Stochastic Processes, Birkhäuser, Cham (2017).
A. N. Borodin, “Distributions of Functionals of Switching Diffusions with Jumps,” Zap. Nauchn. Semin. POMI, 474, 28–45 (2018).
P. Billingsley, Convergence of Probability Measures, John Wiley & Sons Inc., New York, London, Sydney, Toronto (1968).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 474, 2018, pp. 46–62.
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Borodin, A.N. Limit Behavior of a Compound Poisson Process with Switching and Dominated Summands. J Math Sci 251, 27–37 (2020). https://doi.org/10.1007/s10958-020-05061-z
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DOI: https://doi.org/10.1007/s10958-020-05061-z