Existence and Uniqueness of Stationary Lévy-driven CARMA Processes
نویسندگان
چکیده
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 generalize results obtained earlier for second-order processes and for processes defined by the Ornstein-Uhlenbeck equation.
منابع مشابه
Tail Behavior of Multivariate Lévy-Driven Mixed Moving Average Processes and supOU Stochastic Volatility Models
Multivariate Lévy-driven mixed moving average (MMA) processes of the type Xt = ∫ ∫ f(A, t − s)Λ(dA, ds) cover a wide range of well known and extensively used processes such as Ornstein-Uhlenbeck processes, superpositions of Ornstein-Uhlenbeck (supOU) processes, (fractionally integrated) CARMA processes and increments of fractional Lévy processes. In this paper, we introduce multivariate MMA pro...
متن کاملPrediction of Lévy-driven CARMA processes
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...
متن کاملA novel existence and uniqueness theorem for solutions to FDEs driven by Lius process with weak Lipschitz coefficients
This paper we investigate the existence and uniqueness of solutions to fuzzydierential equations driven by Liu's process. For this, it is necessary to provideand prove a new existence and uniqueness theorem for fuzzy dierential equationsunder weak Lipschitz condition. Then the results allows us to considerand analyze solutions to a wide range of nonlinear fuzzy dierential equationsdriven by Liu...
متن کاملEvy - Driven and Fractionally Integrated Armaprocesses with Continuous Time Parameterpeter
The deenition and properties of L evy-driven CARMA (continuous-time ARMA) processes are reviewed. Gaussian CARMA processes are special cases in which the driving L evy process is Brownian motion. The use of more general L evy processes permits the speciication of CARMA processes with a wide variety of marginal distributions which may be asymmetric and heavier tailed than Gaus-sian. Non-negative...
متن کاملEvy Driven and Fractionally Integrated Arma Processes with Continuous Time Parameter
The de nition and properties of L evy driven CARMA continuous time ARMA processes are re viewed Gaussian CARMA processes are special cases in which the driving L evy process is Brownian motion The use of more general L evy processes permits the speci cation of CARMA processes with a wide variety of marginal distributions which may be asymmetric and heavier tailed than Gaus sian Non negative CAR...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009