Martingales and first passage times of AR(1) sequences

DOI10.1080/17442500701840885zbMath1148.60061arXiv0712.3468OpenAlexW1984206429MaRDI QIDQ3498583

N. Kordzakhia, Alexander Novikov

Publication date: 15 May 2008

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.3468

zbMATH Keywords

martingalesfirst passage timesautoregressive processesexponential boundedness

Mathematics Subject Classification ID

Existence theories for optimal control problems involving ordinary differential equations (49J15) Local time and additive functionals (60J55)

Related Items (9)

Probabilistic solutions of integral equations from optimal control ⋮ A general method for finding the optimal threshold in discrete time ⋮ Persistence for a class of order-one autoregressive processes and Mallows-Riordan polynomials ⋮ Pairs trading based on statistical variability of the spread process ⋮ Bounding the Risk Probability ⋮ Persistence Probabilities and Exponents ⋮ Persistence of one-dimensional AR(1)-sequences ⋮ Exit times for ARMA processes ⋮ Exit times for some autoregressive processes with non-Gaussian noise distributions

Cites Work

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• Introductory lectures on fluctuations of Lévy processes with applications.
• Exit times for a class of piecewise exponential Markov processes with two-sided jumps
• On a stochastic difference equation and a representation of non–negative infinitely divisible random variables
• On the First Passage Time of an Autoregressive Process over a Level and an Application to a “Disorder” Problem
• Fluctuation identities for lévy processes and splitting at the maximum
• A Markov Chain Model for the Multivariate Exponentially Weighted Moving Averages Control Chart
• Representations of the First Hitting Time Density of an Ornstein-Uhlenbeck Process¹

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