Ehrenfest–Brillouin-type correlated continuous time random walk and fractional Jacobi diffusion

Leonenko, N.; Papić, I.; Sikorskii, A.; Šuvak, N.

doi:10.1090/tpms/1086

Ehrenfest–Brillouin-type correlated continuous time random walk and fractional Jacobi diffusion

Authors: N. N. Leonenko, I. Papić, A. Sikorskii and N. Šuvak
Journal: Theor. Probability and Math. Statist. 99 (2019), 137-147
MSC (2010): Primary 47D07, 60J10, 60J60, 60G22, 60G50
DOI: https://doi.org/10.1090/tpms/1086
Published electronically: February 27, 2020
MathSciNet review: 3908662
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Abstract: Continuous time random walks (CTRWs) have random waiting times between particle jumps. Based on the Ehrenfest–Brillouin-type model motivated by economics, we define the correlated CTRW that converges to the fractional Jacobi diffusion $Y(E(t))$, $t\ge 0$, defined as a time change of Jacobi diffusion process $Y(t)$ to the inverse $E(t)$ of the standard stable subordinator. In the CTRW considered in this paper, the jumps are correlated so that in the limit the outer process $Y(t)$ is not a Lévy process but a diffusion process with non-independent increments. The waiting times between jumps are selected from the domain of attraction of a stable law, so that the correlated CTRWs with these waiting times converge to $Y(E(t))$.

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