Weighted Sub-fractional Brownian Motion: Covariance Structure, Path Properties and Euler Approximation

Weighted sub-fractional Brownian motion was introduced as a centered Gaussian process with covariance $$ Q_{a,b}(s,t)=\frac{1}{1-b}\int_0^{s\wedge t}u^a[(s-u)^b+(t-u)^b-(s+t-2u)^b]\,du. $$ This kernel was proved to be positive definite for $a>-1$ and $b\in[0,2]\setminus{1}$, and also for $a>-1$,