Condition for intersection occupation measure to be absolutely continuous
DOI:
https://doi.org/10.37863/umzh.v72i9.6278Keywords:
Intersection local time, occupation measure, Plancherel-Parseval theoremAbstract
UDC 519.21
Given the i.i.d. Rd-valued stochastic processes X1(t),…,Xp(t), p≥2, with the stationary increments, a minimal condition is provided for the occupation measure
μt(B)=∫[0,t]p1B(X1(s1)−X2(s2),…,Xp−1(sp−1)−
−Xp(sp))ds1…dsp,B⊂Rd(p−1),
to be absolutely continuous with respect to the Lebesgue measure on Rd(p−1).
An isometry identity related to the resulting density (known as intersection local time) is also established.
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