5 problems

Optimality conjecture. The $h^{1/2}$ rate in the approximation of $Z$ by $Z^{(h)}$ is optimal: the approximation of $Z$ based on sampling $X$ should not be sharper than the approxi…

Let $\psi$ satisfy the growth bounds in \, and let $H(x,v)$ be the function in inequality \. The mesh satisfies $0=t_0\leq t_1\leq\cdots$ with $\delta_k=t_k-t_{k-1}<\delta_0$,…

Let $X$ solve the quasilinear Skorohod SDE … where $X_0\in L^p(\Omega)$ for some $p>2$, $a$ satisfies the global Lipschitz and boundedness condition … for all $t\in[0,1]$,…

Consider the system $\dot{x}=f(x)$, and suppose that $x=0$ is an asymptotically stable equilibrium. Let $\psi(x_0,t)$ denote its solution with initial condition $x_0$, and let…

Let $d$ be the spatial dimension and let $\mathfrak{d}$ denote the spectral measure associated with the homogenization problem. A pair $( u,q)$ is a spectral exponent pair for…