On bivariate distributions of the local time of It\^o-McKean diffusions

Prelegent(ci)

Maciej Wiśniewolski

Afiliacja

Uniwersytet Warszawski

Termin

16 marca 2023 12:15

Pokój

p. 3160

Seminarium

Seminarium Zakładu Rachunku Prawdopodobieństwa

---

Denote as $L$ the local time at $0$ of an It\^o-McKean diffusion $X$. We present a new explicit description of the distribution of $L_t$ in terms of convolution exponent and, using the excursion theory, we describe the transition density of the pair $(X,L)$. We provide a simple connection formula for the distribution of excursions of a bivariate It\^o-McKean diffusion from a hyperplane. Examples involving the distribution of a local time are presented, including a formula for the distribution of $(X_t,L_{\infty})$ for a transient diffusion. Based on joint work with Jacek Jakubowski.

---