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Random walks with sticky barriers
Volume 9, Issue 3 (2022), pp. 245–263
Vladyslav Bohun   Alexander Marynych ORCID icon link to view author Alexander Marynych details  

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https://doi.org/10.15559/22-VMSTA202
Pub. online: 16 March 2022      Type: Research Article      Open accessOpen Access

Received
11 December 2021
Revised
17 February 2022
Accepted
19 February 2022
Published
16 March 2022

Abstract

A new class of multidimensional locally perturbed random walks called random walks with sticky barriers is introduced and analyzed. The laws of large numbers and functional limit theorems are proved for hitting times of successive barriers.

References

[1] 
Bingham, N., Goldie, C., Teugels, J.: Regular Variation vol. 27. Cambridge university press (1989). MR0898871. https://doi.org/10.1017/CBO9780511721434
[2] 
Bohle, D., Marynych, A., Meiners, M.: A fundamental problem of hypothesis testing with finite inventory in e-commerce. Appl. Stoch. Models Bus. Ind. 37(3), 454–474 (2021). MR4274564. https://doi.org/10.1002/asmb.2574
[3] 
Carlsson, H., Nerman, O.: An alternative proof of Lorden’s renewal inequality. Adv. Appl. Probab. 18(4), 1015–1016 (1986). MR0867097. https://doi.org/10.2307/1427260
[4] 
Glynn, P.W., Whitt, W.: Ordinary CLT and WLLN versions of $L=\lambda W$. Math. Oper. Res. 13(4), 674–692 (1988). MR0971918. https://doi.org/10.1287/moor.13.4.674
[5] 
Harrison, J.M., Shepp, L.A.: On skew Brownian motion. Ann. Probab. 9(2), 309–313 (1981). MR0606993
[6] 
Iksanov, A.: Renewal Theory for Perturbed Random Walks and Similar Processes. Probability and Its Applications, p. 250. Birkhäuser (2016). MR3585464. https://doi.org/10.1007/978-3-319-49113-4
[7] 
Iksanov, A., Pilipenko, A.: A functional limit theorem for locally perturbed random walks. Probab. Math. Stat. 36(2), 353–368 (2016). MR3593029
[8] 
Janson, S.: Moments for first-passage and last-exit times, the minimum, and related quantities for random walks with positive drift. Adv. Appl. Probab. 18(4), 865–879 (1986). MR0867090. https://doi.org/10.2307/1427253
[9] 
Minlos, R., Zhizhina, E.: Limit diffusion process for a non-homogeneous random walk on a one-dimensional lattice. Russ. Math. Surv. 52(2), 327 (1997). MR1480138. https://doi.org/10.1070/RM1997v052n02ABEH001778
[10] 
Pilipenko, A., Prikhod’ko, Y.: On the limit behavior of a sequence of Markov processes perturbed in a neighborhood of the singular point. Ukr. Math. J. 67(4), 564–583 (2015). MR3432463. https://doi.org/10.1007/s11253-015-1101-5

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Keywords
Functional limit theorems locally perturbed random walks random walk in a strip random walk with barriers strong laws of large numbers

MSC2010
60J10 60F15 60F17 60G50

Funding
The present work was supported by the National Research Foundation of Ukraine (project 2020.02/0014 «Asymptotic regimes of perturbed random walks: on the edge of modern and classical probability»).

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