TY - JOUR

T1 - Exact formulas in some boundary crossing problems for integer-valued random walks

AU - Lotov, Vladimir Ivanovich

N1 - This work was supported by the Russian Science Foundation (grant no. 22-21-00396). AMS 2020 Mathematics Subject Classification. 60G50.

PY - 2023

Y1 - 2023

N2 - For a wide class of integer-valued random walks, we obtain exact expressions for the distribution of the first excess over level and the corresponding renewal function as well as for the distribution of the trajectory supremum if it is finite. We discuss possibilities of obtaining explicit expressions for pre-stationary and stationary distributions of a random walk with switchings at the strip boundaries. The research is based on the factorization representations for the double moment generating functions of the distributions under study.

AB - For a wide class of integer-valued random walks, we obtain exact expressions for the distribution of the first excess over level and the corresponding renewal function as well as for the distribution of the trajectory supremum if it is finite. We discuss possibilities of obtaining explicit expressions for pre-stationary and stationary distributions of a random walk with switchings at the strip boundaries. The research is based on the factorization representations for the double moment generating functions of the distributions under study.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85168112587&origin=inward&txGid=2a82233e46efb6c2960e46334e56561b

UR - https://www.mendeley.com/catalogue/14fff205-e84b-32c2-99b7-92fbcc5f3496/

U2 - 10.4213/im9323e

DO - 10.4213/im9323e

M3 - Article

VL - 87

SP - 45

EP - 60

JO - Izvestiya Mathematics

JF - Izvestiya Mathematics

SN - 1064-5632

IS - 1

ER -