engleski

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

Continuous time random walks (CTRWs) have random waiting times between particle jumps. Based on Ehrenfest-Brillouin-type model motivated by economics, we define the correlated CTRW that converge to the fractional Jacobi diffusion Y (E(t)), t ≥ 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))

Correlated continuous time random walk ; Ehrenfest-Brillouin Markov chain ; Fractional diffusion ; Jacobi diffusion ; Pearson diffusion

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