In this article we study multivariate continuous-time autoregressive moving-average (MCARMA) processes with values in convex cones. More specifically, introduce matrix-valued MCARMA L\'evy noise and present necessary sufficient conditions for from class to be cone valued. We derive specific hands-on the following two cases: First, classical on $\mathbb{R}_{d}$ positive orthant $\mathbb{R}_{d}^{...

A continuous-state branching process in varying environments is constructed by the pathwise unique positive solution to a stochastic integral equation driven time-space noises. The cumulant semigroup of characterized terms backward equation. We clarify behavior at its bottlenecks, which are deterministic times when it arrives zero almost surely negative jumps. arises naturally as scaling limit ...