TY - JOUR AU - X. Chen PY - 2020/09/22 Y2 - 2024/03/29 TI - Condition for intersection occupation measure to be absolutely continuous JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 72 IS - 9 SE - Research articles DO - 10.37863/umzh.v72i9.6278 UR - https://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 -