All Questions

Normally if you have a linear SDE given such as $dx_t = (A(t)x_t + a(t))dt + \sigma(t) dW_t$, we want to find $x_t$, more precisely we want to find the mean and variance of $x_t$ at each timestep $t$. ...

Let there be two random variables 𝑋 and 𝑌 with a certain joint copula. Is it always true that there is another random variable 𝑍 independent from 𝑌 such as the vectors $(X,Y)$ and $(X,Z)$ have the ...

Let $\lambda_k,\mu_k\in\mathbb R_{\ge0}$ $(k\ge1)$ be nonnegative real numbers, let $S=\mathbb Z_{\ge0}$ be the nonnegative integers, let $T=\mathbb R_{\ge0}$ be the nonnegative real numbers and ...

I am new to probabilistic proofs and trying to understand them better. Apparently, a common probabilistic proof focuses on the existence of expanders (eg. vertex expanders). I've been using the search ...

Under what conditions will a solution $y \in \Re^n$ exist for this system of nonlinear equations? If it exists, will it be unique? $$ \mu_k = \int_0^\infty g_k(x) \, f(x, y) \, dx \qquad \forall \, k ...