Existence and uniqueness of stationary Lévy-driven CARMA processes
نویسندگان
چکیده
منابع مشابه
Existence and Uniqueness of Stationary Lévy-driven CARMA Processes
Necessary and sufficient conditions for the existence of a strictly stationary solution of the equations defining a general Lévy-driven continuous-parameter ARMA process with index set R are determined. Under these conditions the solution is shown to be unique and an explicit expression is given for the process as an integral with respect to the background driving Lévy process. The results gene...
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The conditional expectations, E(Y (h)|Y (u),−∞ < u ≤ 0) and E(Y (h)|Y (u),−M ≤ u ≤ 0) with h > 0 and 0 < M < ∞ are determined for a continuous-time ARMA (CARMA) process (Y (t))t∈R driven by a Lévy process L with E|L(1)| < ∞. If E(L(1)2) <∞ these are the minimum mean-squared error predictors of Y (h) given (Y (t))t≤0 and (Y (t))−M≤t≤0 respectively. Conditions are also established under which the...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2009
ISSN: 0304-4149
DOI: 10.1016/j.spa.2009.01.006