All Questions

Let $Y$ be an infinitely divisible (I.D.) random variable. Let $\nu$ be any measure not necessarily finite: $\nu(\mathbb R)\leq \infty$. Suppose that $Y \sim (0, \nu,0)_0$ according to the notation on ...

I was wondering if there exists an equivalent of a monotone convergence theorem for stochastic integrals. I looked into plenty of books and papers, but I haven't found anything useful. I would expect ...

Assume we have a Levy process $(X_t)_{t\geq 0}$ with a finite second moment for all $t>0$. For simplicity, say $\operatorname{Var}\left[X_1\right]=1$. Let $\tilde{X}_t:=X_t-t\cdot E\left[X_1\right]$...