Higher-Order Derivative of Self-Intersection Local Time for Fractional Brownian Motion

Qian Yu ()
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Qian Yu: Nanjing University of Aeronautics and Astronautics

Journal of Theoretical Probability, 2021, vol. 34, issue 4, 1749-1774

Abstract: Abstract We consider the existence and Hölder continuity conditions for the k-th-order derivatives of self-intersection local time for d-dimensional fractional Brownian motion, where $$k=(k_1,k_2,\ldots , k_d)$$ k = ( k 1 , k 2 , … , k d ) . Moreover, we show a limit theorem for the critical case with $$H=\frac{2}{3}$$ H = 2 3 and $$d=1$$ d = 1 , which was conjectured by Jung and Markowsky [7].

Keywords: Self-intersection local time; Fractional Brownian motion; Hölder continuity; 60G22; 60J55 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-021-01093-6

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