Given i.i.d. ℝ^d-valued stochastic processes X₁(t), . . . ,X_p(t), p ≥ 2, with stationary increments, a minimal condition is provided for the occupation measure

\( {\mu}_t(B)=\underset{\left[0,t\right]}{\int }1B\left({X}_1\left({s}_1\right)-{X}_2\left({s}_2\right),\dots, {X}_{p-1}\left({s}_{p-1}\right)-{X}_p\left({s}_p\right)\right){ds}_1\dots {ds}_p, \) B ⊂ ℝ^d(p−1),

to be absolutely continuous with respect to the Lebesgue measure on ℝ^d(p−1). An isometry identity related to the resulting density (known as intersection local time) is also established.

鉴于IIDℝ ^d -valued随机过程X ₁（吨），。。。中，X _p（吨），对≥ 2 ，具有固定的增量，提供了用于占用度量的最小条件

\（{\ mu} _t（B）= \ underset {\ left [0，t \ right]} {\ int} 1B \ left（{X} _1 \ left（{s} _1 \ right）-{X} _2 \ left（{s} _2 \ right），\ dots，{X} _ {p-1} \ left（{s} _ {p-1} \ right）-{X} _p \ left（{s} _p \右）\右）{DS} _1 \点{DS} _p，\） 乙⊂ℝ ^{d（对- 1）}，

是相对于所述Lebesgue测度上ℝ绝对连续^{d（对- 1）} 。还建立了与所得密度（称为交点本地时间）相关的等距线身份。