All Questions

I am interested in the following time-invariant multivariate SDE: \begin{equation} dx_i = \sum_{j} a_{ij} x_j\,dt + \sum_{j,k} b_{ijk} x_k \, dW_j \end{equation} Despite its simplicity the general ...

Consider the following paper titled: Stochastic regime switching SIR model driven by Lévy noise, authored by Yingjia Guo. Link: https://www.sciencedirect.com/science/article/pii/S0378437117302145 The ...

Let $h\in C^1(\mathbb R)$ such that $h'$ is Lipschitz continuous and $$L\varphi:=-h'\varphi'+\varphi''\;\;\;\text{for }\varphi\in C^2(\mathbb R).$$ The formal adjoint of $L$ is $$L^\ast\psi:=\psi''+(h'...

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 ...