4 problems

Long range dependence conjecture. The moving average $X$ is long range dependent if and only if

Let $L$ be a Lévy process without the symmetry assumption, let $X$ be the corresponding Lévy-driven moving average, and consider the limiting distribution in the asymptotic framewo…

Let $X$ be a stationary-increments Lévy-driven moving average whose small-scale tangent process is the symmetric fractional $\beta$-stable motion described above, and let $L$ be th…

Let $(X_i)$ be a moving-average process with coefficients $(\varphi_j)_{j\in\mathbb Z}$, and let … varphij=0quadtext{for }j<0, … 0leqslant frac{sum{j=0}^{K}varphij}{sum{j=0}^{infty…