Vector valued unified martingale and ergodic theorems with continuous\n parameter

2020/02/15 by Farruh Shahidi, Shahidi, Farruh
Economics, Econometrics and Finance · Mathematics · #Advanced Banach Space Theory #Dynamical Systems (math.DS) #Economic theories and models #FOS: Mathematics #Housing Market and Economics

paper · pdf · doi:10.48550/arxiv.2002.06399

openalex publication_date 2020/02/15 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We prove martingale-ergodic and ergodic-martingale theorems with continuous\nparameter for vector valued Bochner integrable functions. We first prove almost\neverywhere convergence of vector valued martingales with continuous parameter.\nThe norm as well as almost everywhere convergence of martingale-ergodic and\nergodic-martingale averages are given. We also obtain the dominant and maximal\ninequalities. Finally, we show that a.e. martingale-ergodic and\nergodic-martingale theorems will coincide under certain assumptions.\n

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