# Effective Complexity of Stationary Process Realizations

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## Abstract

**:**

## 1. Introduction

## 2. Notations and Preliminaries

## 3. Effective Complexity of Stationary Processes

**Theorem 1.**Let P be a stationary process, $\delta \ge 0$, $\u03f5>0$ and ${\Delta}_{n}=\u03f5n$. Then P is effectively simple in the sense that for P-almost every x,

## 4. Coarse Effective Complexity

**Proposition 2.**Let $\delta \ge 0$. There is a constant c such that for all $x\in {\{0,1\}}^{*}$ we have

**Theorem 3.**Let $\delta \ge 0$. For every sufficiently large $n\in \mathbb{N}$ there exists a string $x\in {\{0,1\}}^{n}$ with

**Theorem 4.**Let P be a stationary process, $\delta \ge 0$ and $\u03f5>0$. Then for P-almost every x

## 5. Conclusions

## Acknowledgements

## References

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**MDPI and ACS Style**

Ay, N.; Müller, M.; Szkoła, A.
Effective Complexity of Stationary Process Realizations. *Entropy* **2011**, *13*, 1200-1211.
https://doi.org/10.3390/e13061200

**AMA Style**

Ay N, Müller M, Szkoła A.
Effective Complexity of Stationary Process Realizations. *Entropy*. 2011; 13(6):1200-1211.
https://doi.org/10.3390/e13061200

**Chicago/Turabian Style**

Ay, Nihat, Markus Müller, and Arleta Szkoła.
2011. "Effective Complexity of Stationary Process Realizations" *Entropy* 13, no. 6: 1200-1211.
https://doi.org/10.3390/e13061200