On the Family of First Passage Time of a Parabola by the Markov Perturbed Random Walk Described by an Autoregressive Process AR(1).

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Fərhadova A., Rəhimov F., Əliyev R.

The 9 International Conference on Control and Optimization with Industrial Applications, no.1, pp.745-748, 2025 (Conference Book)

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In this paper, consider a family of the first passage times of parabolic boundary by Markov perturbed random walk, described first-order autoregressive process AR(1). The uniform integrability property, asymptotic behavior of expectation and variance of this family are studied