Limit theorems for a random walk with memory perturbed by a dynamical system

  • Cristian F. Coletti, Lucas R. de Lima, Renato J. Gava, Denis A. Luiz
  • Journal of Mathematical Physics, October 2020, American Institute of Physics
  • DOI: 10.1063/5.0014940

What is it about?

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.

Read Publication

http://dx.doi.org/10.1063/5.0014940

The following have contributed to this page: Renato Gava and Lucas R. de Lima

In partnership with:

Link to American Institute of Physics showcase

join the fight against climate change

Our simple summaries of climate research help you take action

Read now

climate-change.info