# Vector valued unified martingale and ergodic theorems with continuous parameter

@article{Shahidi2020VectorVU, title={Vector valued unified martingale and ergodic theorems with continuous parameter}, author={Farruh Shahidi}, journal={arXiv: Dynamical Systems}, year={2020} }

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…

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## References

SHOWING 1-10 OF 20 REFERENCES

### Vector Valued Martingale-Ergodic and Ergodic-Martingale Theorems

- Mathematics
- 2012

We prove martingale-ergodic and ergodic-martingale theorems for vector-valued Bochner integrable functions. We obtain dominant and maximal inequalities. We also prove weighted and multiparameter…

### On multiparameter ergodic and martingale theorems in infinite measure spaces

- Mathematics
- 1986

SummaryA unified proof is given of several ergodic and martingale theorems in infinite measure spaces.

### Mean Ergodic Theorems in Hilbert-Kaplansky spaces

- Mathematics
- 2012

We prove the mean ergodic theorem of von Neumann in a Hilbert-Kaplansky space. We also prove a multiparameter, modulated, subsequential and a weighted mean ergodic theorems in a Hilbert-Kaplansky…

### Ergodic properties of contraction semigroups in Lp,1 < p < ∞

- Mathematics
- 1994

Let {T(t) : t > 0} be a strongly continuous semigroup of linear contractions in Lp, 1 0 a positive linear contraction P(t) in Lp such that |T(t)f | ≤ P(t)|f | for all f ∈ Lp, then there exists a…

### Forcing Divergence When the Supremum Is Not Integrable

- Mathematics
- 2006

If a sequence of functions (fn) has an integrable supremum and converges almost everywhere, then an operator sequence (Tn) will yield a sequence (Tnfn) that converges almost everywhere too, under…

### On vector measures

- Mathematics
- 1974

The four sections of this paper treat four different but somewhat related topics in the theory of vector measures. In §1 necessary and sufficient conditions for a Banach space X to have the property…

### General theories unifying ergodic averages and martingales

- Mathematics
- 2007

The curious fact that the behavior of ergodic averages is analogous to the behavior of (reversed) martingales has long been known. For the last 60 years, at least five different approaches have been…

### Stochastic differential equations : an introduction with applications

- Mathematics
- 1987

Some Mathematical Preliminaries.- Ito Integrals.- The Ito Formula and the Martingale Representation Theorem.- Stochastic Differential Equations.- The Filtering Problem.- Diffusions: Basic…

### Martingale-ergodic and ergodic-martingale processes with continuos parameter

- Mt. Sb.,
- 2009