Discrete Random Processes with Memory: Models and Applications


The contribution focuses on Bernoulli-like random walks, where the past events significantly affect the walk’s future development. The main concern of the paper is therefore the formulation of models describing the dependence of transition probabilities on the process history. Such an impact can be incorporated explicitly and transition probabilities modulated using a few parameters reflecting the current state of the walk as well as the information about the past path. The behavior of proposed random walks, as well as the task of their parameter estimation, are studied both theoretically and with the aid of simulations.

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Corresponding authors

Correspondence to Tomáš Kouřim or Petr Volf.

Additional information

The research was supported by the grant No. 18-02739S of the Grant Agency of the Czech Republic.

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Kouřim, T., Volf, P. Discrete Random Processes with Memory: Models and Applications. Appl Math 65, 271–286 (2020). https://doi.org/10.21136/AM.2020.0335-19

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  • random walk
  • history dependent transition probability
  • non-Markov process
  • success punishing walk
  • success rewarding walk

MSC 2020

  • 60G50
  • 62F10