@article{Chen_2020, title={Condition for intersection occupation measure to be absolutely continuous }, volume={72}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/6278}, DOI={10.37863/umzh.v72i9.6278}, abstractNote={<p>UDC 519.21</p> <p>Given 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<br>$$\mu_t(B)=\int\limits _{[0,t]^p}1_B\big(X_1(s_1) - X_2(s_2),\ldots, X_{p-1}(s_{p-1}) -$$</p> <p>$$- X_p(s_p)\big)ds_1\ldots ds_p,\quad B\subset \mathbb{R}^{d(p-1)},$$<br>to be absolutely continuous with respect to the Lebesgue measure on $\mathbb{R}^{d(p-1)}.$ <br>An isometry identity related to the resulting density (known as intersection local time) is also established.</p&gt;}, number={9}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Chen, X.}, year={2020}, month={Sep.}, pages={1304-1312} }