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

References:

[1] Davis, R. A., Liu, H.: **Theory and inference for a class of nonlinear models with application to time series of counts**. Stat. Sin. 26 (2016), 1673-1707. DOI 10.5705/ss.2014.145t | MR 3586234 | Zbl 1356.62137

[2] Feller, W.: **An Introduction to Probability Theory and Its Applications**. A Wiley Publication in Mathematical Statistics. John Wiley & Sons, New York (1957). MR 0088081 | Zbl 0077.12201

[3] Hawkes, A. G.: **Spectra of some self-exciting and mutually exciting point processes**. Biometrika 58 (1971), 83-90. DOI 10.1093/biomet/58.1.83 | MR 0278410 | Zbl 0219.60029

[4] Kouřim, T.: **Random walks with varying transition probabilities**. Doktorandské dny 2017 P. Ambrož, Z. Masáková ČVUT, FJFI, Praha (2017), 141-150.

[5] Kouřim, T.: **Random walks with memory applied to grand slam tennis matches modeling**. MathSport International 2019: Conference Proceedings Propobos Publications, Athens (2019), 220-227.

[6] Kouřim, T.: **Statistical Analysis, Modeling and Applications of Random Processes with Memory: PhD Thesis Study**. ČVUT FJFI, Praha (2019). MR 4114252

[7] Pearson, K.: **The problem of the random walk**. Nature 72 (1905), 342 \99999JFM99999 36.0303.02. DOI 10.1038/072342a0

[8] Rossi, R. J.: **Mathematical Statistics: An Introduction to Likelihood Based Inference**. John Wiley & Sons, Hoboken (2018). DOI 10.1002/9781118771075 | Zbl 1407.62006

[9] Schütz, G. M., Trimper, S.: **Elephants can always remember: Exact long-range memory effects in a non-Markovian random walk**. Phys. Rev. E 70 (2004), Article ID 045101. DOI 10.1103/PhysRevE.70.045101

[10] Turban, L.: **On a random walk with memory and its relation with Markovian processes**. J. Phys. A, Math. Theor. 43 (2010), Article ID 285006, 9 pages. DOI 10.1088/1751-8113/43/28/285006 | MR 2658904 | Zbl 1204.82022