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In this paper, sufficient conditions are given for the existence of limiting distribution of a conservative affine process on the canonical state space $\mathbb{R}_{\geqslant0}^{m}\times\mathbb{R}^{n}$, where $m,\thinspace n\in\mathbb{Z}_{\geqslant0}$ with $m+n>0$. Our… Click to show full abstract
In this paper, sufficient conditions are given for the existence of limiting distribution of a conservative affine process on the canonical state space $\mathbb{R}_{\geqslant0}^{m}\times\mathbb{R}^{n}$, where $m,\thinspace n\in\mathbb{Z}_{\geqslant0}$ with $m+n>0$. Our main theorem extends and unifies some known results for OU-type processes on $\mathbb{R}^{n}$ and one-dimensional CBI processes (with state space $\mathbb{R}_{\geqslant0}$). To prove our result, we combine analytical and probabilistic techniques; in particular, the stability theory for ODEs plays an important role.
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2020
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