Existence and uniqueness of stationary Lévy-driven CARMA processes

Stochastic Processes and their Applications

Volumn 119, Issue 8, 2009, Pages 2660-2681

  Brockwell, Peter J ^a   Lindner, Alexander ^b  

^a Veterinary Dentistry and Oral Surgery   (United States)

^b TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

Author keywords

CARMA process; Causality; L vy process; State space representation; Stationarity; Stochastic differential equation

Indexed keywords

CARMA PROCESS; CAUSALITY; STATE-SPACE REPRESENTATION; STATIONARITY; STOCHASTIC DIFFERENTIAL EQUATION;

MEASUREMENT THEORY; RANDOM PROCESSES; STOCHASTIC CONTROL SYSTEMS;

DIFFERENTIAL EQUATIONS;

EID: 67349276975     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2009.01.006     Document Type: Article

References (13)

1. Brockwell P.J., and Davis R.A. Time Series: Theory and Methods. 2nd ed. (1991), Springer-Verlag, New York
2. Brockwell P.J. Continuous-time ARMA Processes. In: Shanbhag D.N., and Rao C.R. (Eds). Handbook of Statistics 19; Stochastic Processes: Theory and Methods (2001), Elsevier, Amsterdam 249-276
3. Brockwell P.J., and Marquardt T. Fractionally integrated continuous-time ARMA processes. Statist. Sinica 15 (2005) 477-494
4. Brockwell P.J. Lévy-driven CARMA processes. Ann. Inst. Stat. Math. 53 (2001) 113-124
5. n. Stochastic Process. Appl. 12 (1982) 301-312
6. Sato K., and Yamazato M. Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type. Stochastic Process. Appl. 17 (1984) 73-100
7. Bernstein D.S. Matrix Mathematics: Theory, Facts, and Formulas with application to linear systems theory (2005), Princeton University Press, Princeton
8. Eller J. On functions of companion matrices. Linear Algebra Appl. 96 (1987) 191-210
9. Tsai H., and Chan K.-S. A note on the non-negativity of continuous-time ARMA and GARCH processes. Statistics and Computing 19 (2009) 149-153
10. Sato K. Lévy processes and infinitely divisible distributions (1999), Cambridge University Press, Cambridge
11. Kallenberg O. Foundations of Modern Probability. 2nd ed. (2002), Springer-Verlag, New York
12. Sato K. Two families of improper stochastic integrals with respect to Lévy processes. ALEA 1 (2006) 47-87
13. Sato K. Monotonicity and non-monotonicity of domains of stochastic integral operators. Probab. Math. Statist. 26 (2006) 23-39