Kavli Affiliate: Ran Wang
| First 5 Authors: Mengjie Lyu, Min Wang, Ran Wang, ,
| Summary:
Let ${X(t)}_{tgeqslant0}$ be the generalized fractional Brownian motion
introduced by Pang and Taqqu (2019):
begin{align*}
{X(t)}_{tge0}overset{d}{=}&left{ int_{mathbb R}
left((t-u)_+^{alpha}-(-u)_+^{alpha} right) |u|^{-gamma/2}
B(du) right}_{tge0},
end{align*} where $ gammain [0,1), alphain
left(-frac12+frac{gamma}{2}, frac12+frac{gamma}{2} right)$ are
constants. For any $theta>0$, let begin{align*}
Y(t)=frac{1}{Gamma(theta)}int_0^t (t-u)^{theta-1} X(u)du, quad tge 0.
end{align*} Building upon the arguments of Talagrand (1996), we give integral
criteria for the lower classes of $Y$ at $t=0$ and at infinity, respectively.
As a consequence, we derive its Chung-type laws of the iterated logarithm. In
the proofs, the small ball probability estimates play important roles.
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