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Let $E$ be a separable $\mathbb R$-Banach space, $v:E\to[1,\infty)$ be continuous, $$\rho(x,y):=\inf_{\substack{\gamma\:\in\:C^1([0,\:1],\:E)\\ \gamma(0)\:=\:x\\ \gamma(1)\:=\:y}}\int_0^1v\left(\gamma(...

I asked this problem on MSE some while ago, but it has stubbornly resisted any attempts at solving it. Maybe there is someone here who can either close the gap in one of the existing answers or has ...

I'm looking for results on the stability of stochastic systems, e.g. SDEs, whose coefficients depend on a different process that is not necessarily stable. I'm calling those systems "open" here, but ...

How to prove uniqueness of the stationary measure using coupling approach to the following process: $u_{n+1}=S(1)u_n+\eta_{n+1}(\omega)$, where a) $S(1)y_0:=y(1)$, $y(t)$ solves the following Cauchy ...