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For each $x\in R^d$, let $\nu(x,dz)$ be a L\'evy measure, i.e., $$ \int_{R^d}(|z|^2\wedge1)\nu(x,dz)<\infty. $$ Let $\mu$ be a probability measure on $R^d$ such that $$ \int_{R^d}\int_{R^d}(|z|^2\...

Let $X = (X_1, X_2, \ldots , X_n)$ be an $n$-dimensional random variable, where each $X_i$ is a random variable on finite discrete set $S$. In addition, $X_i$ are independent of each other (but not ...

Suppose we want to approximate a real-valued random variable $X$ by a discrete random variable $Z$ with finitely many atoms. Suppose all moments of $X$ is finite. We want to match the moments of $X$ ...