Martingales and first passage times of AR(1) sequences

2007/12/20 by А. А. Новиков, Novikov, Alexander, Nino Kordzakhia +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · #34A30 #49J15 #60J55 #Approximation Theory and Sequence Spaces #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0712.3468

openalex publication_date 2007/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the martingale approach we find sufficient conditions for exponential boundedness of first passage times over a level for ergodic first order autoregressive sequences (AR(1)). Further, we prove a martingale identity to be used in obtaining explicit bounds for the expectation of first passage times.

Cited by

• Persistence probabilities of MA(1) sequences with Laplace innovations and q-deformed zigzag numbers
• Persistence probabilities for MA(1) sequences with uniform innovations

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