Vector valued unified martingale and ergodic theorems with continuous parameter

Farruh Shahidi

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arXiv · 2002.06399

Vector valued unified martingale and ergodic theorems with continuous parameter

Farruh Shahidi

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Abstract

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

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Farruh Shahidi. 2020-02-15. Vector valued unified martingale and ergodic theorems with continuous parameter. https://arxiv.org/abs/2002.06399

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