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On the collision local time of sub-fractional Brownian motions. (English) Zbl 1185.60040

Summary: Let S H i ={S t H i ,t0},i=1,2, be two independent sub-fractional Brownian motions with respective indices H i (0,1). We consider the so-called collision local time

T = 0 T δ(S t H 1 -S t H 2 )dt,T>0,

where δ denotes the Dirac delta function. By an elementary method we show that T is smooth in the sense of Meyer and Watanabe if and only if min{H 1 ,H 2 }<1/3·

60G22Fractional processes, including fractional Brownian motion
60G15Gaussian processes
60G18Self-similar processes
60F25L p -limit theorems (probability)
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