Naslov
Correlated Continuous Time Random Walks and Pearson Diffusions

Autori
Leonenko, Nikolai ; Papić, Ivan ; Sikorskii, Alla ; Šuvak, Nenad

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Skup
22nd Young Statisticians Meeting

Mjesto i datum
Zagreb, Hrvatska, 13.10.2017. - 15.10.2017

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

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

Sažetak
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.

Izvorni jezik
Engleski

POVEZANOST RADA