Аннотация:
В работе найдена асимптотика и получены оценки для
распределения времен первого прохождения нулевого
уровня (в обоих направлениях) случайным блужданием
с ненулевым сносом.
Библиография: 22 названия.
Ion Grama, Hui Xiao, “Conditioned local limit theorems for random walks on the real line”, Ann. Inst. H. Poincaré Probab. Statist., 61:1 (2025)
ION GRAMA, JEAN-FRANÇOIS QUINT, HUI XIAO, “Conditioned limit theorems for hyperbolic dynamical systems”, Ergod. Th. Dynam. Sys., 44:1 (2024), 50
Grama I., Lauvergnat R., Le Page E., “Conditioned Local Limit Theorems For Random Walks Defined on Finite Markov Chains”, Probab. Theory Relat. Field, 176:1-2 (2020), 669–735
Berger Q., “Notes on Random Walks in the Cauchy Domain of Attraction”, Probab. Theory Relat. Field, 175:1-2 (2019), 1–44
Grama I., Lauvergnat R., Le Page E., “Limit Theorems For Markov Walks Conditioned to Stay Positive Under a Spectral Gap Assumption”, Ann. Probab., 46:4 (2018), 1807–1877
Ion Grama, Ronan Lauvergnat, Émile Le Page, “Limit theorems for affine Markov walks conditioned to stay positive”, Ann. Inst. H. Poincaré Probab. Statist., 54:1 (2018)
Р. T. Алиев, Т. А. Ханиев, “О предельном поведении характеристической функции эргодического распределения полумарковского процесса с двумя границами”, Матем. заметки, 102:4 (2017), 490–502; R. T. Aliev, T. A. Khaniev, “On the Limiting Behavior of the Characteristic Function of the Ergodic Distribution of the Semi-Markov Walk with Two Boundaries”, Math. Notes, 102:4 (2017), 444–454
Grama I., Le Page E., Peigne M., “Conditioned Limit Theorems For Products of Random Matrices”, Probab. Theory Relat. Field, 168:3-4 (2017), 601–639
Ion Grama, Springer Proceedings in Mathematics & Statistics, 208, Modern Problems of Stochastic Analysis and Statistics, 2017, 93
Ion Grama, Émile Le Page, Springer Proceedings in Mathematics & Statistics, 208, Modern Problems of Stochastic Analysis and Statistics, 2017, 103
Aurzada F., Kramm T., “The First Passage Time Problem Over a Moving Boundary for Asymptotically Stable Lévy Processes”, J. Theor. Probab., 29:3 (2016), 737–760
Aurzada F., Kramm T., Savov M., “First Passage Times of Levy Processes Over a One-Sided Moving Boundary”, Markov Process. Relat. Fields, 21:1 (2015), 1–38
Denisov D., Shneer V., “Asymptotics for the First Passage Times of Levy Processes and Random Walks”, J. Appl. Probab., 50:1 (2013), 64–84
T. I. Nasirova, M. N. Mikailov, “Analysis of the distribution of a random process with differential semi-Markov walk with delaying screen at zero”, Cybern Syst Anal, 49:3 (2013), 441
Denis Denisov, Vsevolod Shneer, “Asymptotics for the First Passage Times of Lévy Processes and Random Walks”, J. Appl. Probab., 50:01 (2013), 64
Vatutin V.A., Wachtel V., “Local probabilities for random walks conditioned to stay positive”, Probab. Theory Related Fields, 143:1-2 (2009), 177–217
А. А. Могульский, “О больших уклонениях времени первого прохождения для случайного блуждания с семиэкспоненциально распределенными скачками”, Сиб. матем. журн., 47:6 (2006), 1323–1341; A. A. Mogul'skii, “Large deviations of the first passage time for a random walk with semiexponentially distributed jumps”, Siberian Math. J., 47:6 (2006), 1084–1101
А. А. Могульский, Б. А. Рогозин, “Локальная теорема для момента достижения фиксированного уровня случайным блужданием”, Матем. тр., 8:1 (2005), 43–70; A. A. Mogul'skii, B. A. Rogozin, “A Local Theorem for the First Hitting Time of a Fixed Level by a Random Walk”, Siberian Adv. Math., 15:3 (2005), 1–27