Limit theorems for a random walk with memory perturbed by a dynamical system
| Autor: | Denis A. Luiz, Cristian F. Coletti, Lucas R. de Lima, Renato J. Gava |
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| Rok vydání: | 2020 |
| Předmět: |
Stochastic process
010102 general mathematics Probability (math.PR) Statistical and Nonlinear Physics Law of the iterated logarithm Dynamical system Random walk 01 natural sciences Distribution (mathematics) Law of large numbers 0103 physical sciences FOS: Mathematics 010307 mathematical physics Limit (mathematics) Statistical physics 0101 mathematics Mathematics - Probability Mathematical Physics Central limit theorem Mathematics |
| DOI: | 10.48550/arxiv.2005.07288 |
| Popis: | We introduce a new random walk with unbounded memory obtained as a mixture of the Elephant Random Walk and the Dynamic Random Walk which we call the Dynamic Elephant Random Walk (DERW). As a consequence of this mixture the distribution of the increments of the resulting random process is time dependent. We prove a strong law of large numbers for the DERW and, in a particular case, we provide an explicit expression for its speed. Finally, we give sufficient conditions for the central limit theorem and the law of the iterated logarithm to hold. Comment: We corrected a typo in the definition of the ERW |
| Databáze: | OpenAIRE |
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