Ergodic Properties of generalized Ornstein – Uhlenbeck Processes
Theory and Applications of Mathematical Science Vol. 3,
Page 84-105
Abstract
Let an -valued random process ξ be the solution of an equation of the kind ξ(t) = ξ(0) +, where ξ(0) is a random variable measurable w. r. t. some σ-algebra , S is a random process with-conditionally independent increments, ι is a continuous numeral random process of locally bounded variation, and A is a matrix-valued random process such that for any. Conditions guaranteing the existence of the limiting, as t → ∞, distribution of ξ(t) are found. The characteristic function of this distribution is written explicitly. An ergodic theorem for generalized Ornstein – Uhlenbeck processes is proved.
Keywords:
- Limit distribution; generalized Ornstein { Uhlenbeck processes
- process
- ergodic theorem.
How to Cite
Yurachkivsky, A. (2020). Ergodic Properties of generalized Ornstein – Uhlenbeck Processes. Theory and Applications of Mathematical Science Vol. 3, 84-105. Retrieved from https://stm1.bookpi.org/index.php/tams-v3/article/view/1113
- Abstract View: 0 times