engleski

Correlated Continuous Time Random Walks and Pearson Diffusions

Continuous time random walks have random waiting times between particle jumps. We define the correlated continuous time random walks (CTRWs) that converge to Pearson diffusions. Pearson diffusions have stationary distributions of Pearson type (i.e. normal, gamma, beta, Fisher- Snedecor, reciprocal gamma or Student stationary distribution). The jumps in these CTRWs are obtained from Markov chains through the Bernoulli urn- scheme model and Wright-Fisher model. The jumps are correlated so that the limiting processes are not Lévy but diffusion processes with nonindependent increments. According to the carefully chosen starting Markov chain, different limiting Pearson diffusions can be obtained. We present Ornstein-Uhlenbeck (OU) process, Cox- Ingersol- Ross (CIR) and Jacobi diffusion as the limiting Pearson diffusions.

Markov chains ; diffusions ; Pearson diffusions ; urnscheme models ; Wright-Fisher model ; continuous time random walks

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