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If random variable $X$ has a probability distribution of $f(x)$ and random variable $Y$ has a probability distribution $g(x)$ then $(f*g)(x)$, the convolution of $f$ and $g$, is the probability ...

Suppose $f$ is a continuous function on $\mathbb{R}^n$, and $W$ has a multivariate normal distribution on $\mathbb{R}^n$. If the expectation $$g(v)=\mathbb{E}[f(v+W)]$$ is defined for all $v \in \...

Suppose $X, Y$ are two independent non-negative random variables. The conditions (i) $\mathbb{P}(X > t) = \frac{C}{t^p} + o(t^{-p})$ (ii) $\mathbb{P}(Y > t) = o(t^{-q})$ for any $q > ...