We find a stationary distribution of a stochastic process with delay at the origin. The trajectories of the process have linear growth and random jumps at random times. We use known results for regenerative processes and factorization technique for the study in boundary crossing problems for random walks.
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Translated from Sibirskii Zhurnal Chistoi i Prikladnoi Matematiki 17, No. 1, 2017, pp. 36-44.
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Lotov, V.I., Okhapkina, E.M. Stationary Distribution of a Stochastic Process. J Math Sci 231, 218–226 (2018). https://doi.org/10.1007/s10958-018-3817-x
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DOI: https://doi.org/10.1007/s10958-018-3817-x