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math.PR2026
On the Absolute-Value Integral of a Brownian Motion with Drift: Exact and Asymptotic Formulae
Weixuan Xia, Yuyang Zhang
The present paper is concerned with the integral of the absolute value of a Brownian motion with drift. By establishing an asymptotic expansion of the space Laplace transform, we o…
math.PR2025
On certain integral functionals of integer-valued subordinators
Dongdong Hu, Hasanjan Sayit, Weixuan Xia
It is known that the exponential functional of a Poisson process admits a probability density function in the form of an infinite series. In this paper, we obtain an explicit expre…
math.PR2024
Set-valued stochastic integrals for convoluted Lévy processes
Weixuan Xia
In this paper we study set-valued Volterra-type stochastic integrals driven by Lévy processes. Upon extending the classical definitions of set-valued stochastic integral functiona…