TY - JOUR
AU - X. Chen
PY - 2020/09/22
Y2 - 2020/10/30
TI - Condition for intersection occupation measure to be absolutely continuous
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 72
IS - 9
SE - Research articles
DO - 10.37863/umzh.v72i9.6278
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/6278
AB - UDC 519.21Given the i.i.d. $\mathbb{R}^d$-valued stochastic processes $X_1(t),\ldots, X_p(t),$ $p\ge 2,$ with the stationary increments, a minimal condition is provided for the occupation measure$$\mu_t(B)=\int\limits _{[0,t]^p}1_B\big(X_1(s_1) - X_2(s_2),\ldots, X_{p-1}(s_{p-1}) -$$$$- X_p(s_p)\big)ds_1\ldots ds_p,\quad B\subset \mathbb{R}^{d(p-1)},$$to be absolutely continuous with respect to the Lebesgue measure on $\mathbb{R}^{d(p-1)}.$ An isometry identity related to the resulting density (known as intersection local time) is also established.
ER -