“…Note 2. Note that Theorem 2 for an ordinary random walk formed by sums of independent random variables was proved in [13]. Note also that similar theorems were proved in [14] for the case when the random walk is described by the trajectories of the Markov chain.…”
The consider one family of first passage times of a Markov random walk described by a first-order autoregressive process AR(1) for nonlinear boundaries. Limit theorems are proved for a Markov random walk and a family of first passage times of this walk for nonlinear boundaries.
“…Note 2. Note that Theorem 2 for an ordinary random walk formed by sums of independent random variables was proved in [13]. Note also that similar theorems were proved in [14] for the case when the random walk is described by the trajectories of the Markov chain.…”
The consider one family of first passage times of a Markov random walk described by a first-order autoregressive process AR(1) for nonlinear boundaries. Limit theorems are proved for a Markov random walk and a family of first passage times of this walk for nonlinear boundaries.
В работе при условиях, близких к минимальным, найдены локальная и интегральная асимптотики для совместного распределения времени первого прохождения случайным блужданием произвольной удаленной границы и величины перескока через эту границу.
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