Higher-Order Derivative of Intersection Local Time for Two Independent Fractional Brownian Motions

Jingjun Guo (), Yaozhong Hu and Yanping Xiao
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Jingjun Guo: Lanzhou University of Finance and Economics
Yaozhong Hu: University of Alberta
Yanping Xiao: Northwest Minzu University

Journal of Theoretical Probability, 2019, vol. 32, issue 3, 1190-1201

Abstract: Abstract In this article, we obtain sharp conditions for the existence of the high-order derivatives (k-th order) of intersection local time $$ \widehat{\alpha }^{(k)}(0)$$ α ^ ( k ) ( 0 ) of two independent d-dimensional fractional Brownian motions $$B^{H_1}_t$$ B t H 1 and $$\widetilde{B}^{H_2}_s$$ B ~ s H 2 of Hurst parameters $$H_1$$ H 1 and $$H_2$$ H 2 , respectively. We also study their exponential integrability.

Keywords: Fractional Brownian motion; Intersection local time; k-th derivative of intersection local time; Exponential integrability; 60G22; 60J55 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10959-017-0800-2

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