Limit Distribution of a Generalized Ornstein -- Uhlenbeck Process
- Andriy Yurachkivsky
AbstractLet an $\bR^d$-valued random process $\xi$ be the solution of an equation of the kind $\xi(t)=\xi(0)+\int_0^tA(u)\xi(u)\rd\iota(u)+S(t),$ where $\xi(0)$ is a random variable measurable w.\,r.\,t. some $\sigma$-algebra $\cF(0)$, $S$ is a random process with $\cF(0)$-conditionally independent increments, $\iota$ is a continuous numeral random process of locally bounded variation, and $A$ is a matrix-valued random process such that for any $t>0$ $\int_0^t\|A(s)\|\ |\rd\iota(s)|<\iy.$ Conditions guaranteing existence of the limiting, as $t\to\iy$, distribution of $\xi(t)$ are found. The characteristic function of this distribution is written explicitly.
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