Multivariate continuous-time autoregressive moving-average processes on cones

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 $\mathbb{R}_{d}^{+}$. Second, real square matrices taking of symmetric semi-definite matrices. Both cases are relevant applications give several examples positivity ensuring parameter specifications. addition above, discuss capability model spot covariance process stochastic volatility models. justify relevance based models by an exemplary analysis second order structure well-balanced Ornstein-Uhlenbeck