Barndor -Nielsen, O.E.: Superposition of Ornstein-Uhlenbeck type processes. Theory Probab. Appl. 45, 175-194 (2001) Home/Search Document Not in Database Summary Related Articles Check |
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Stochastic Models That Separate Fractal Dimension and Hurst.. - Gneiting, Schlather (2003) (Correct)
...., h . 11) Any combination of the parameters # (0, 2] and # 0 is permissible. The Cauchy class provides flexible power law correlations and generalizes stochastic models recently discussed and synthesized in geostatistics [7, 42] physics [24, 33] hydrology [23] and time series analysis [3, 17]. These works consider time series in discrete time only, or they restrict # to 1 or 2. The special case # = 2 has been known as Cauchy model [7, 42] and we refer to the general case, # (0, 2] as Cauchy class. Arguments in analogy to those in [17] and references therein show that # (0, 2] ....
O. E. Barndor#-Nielsen, Superposition of Ornstein-Uhlenbeck type processes, Theory of Probability and its Applications, 45 (2000), pp. 175--194.
Optimal Portfolio Problems In Lévy Markets - Benth, Karlsen, Reikvam (Correct)
....normal invers Gaussian L evy process, the long range dependency structure observed in data is not explained. Even though the geometric normal invers Gaussian L evy process gives a good description for the marginals, new models are called for. Barndor Nielsen and Shepard [5] see also [6] and [4]) have recently suggested a class of stochastic volatility models where the risky asset follows the dynamics d ln S t = t dt p t dW t (4.1) and d t = t dt dL t ; 4.2) L t being a driftless pure jump L evy process with non negative increments independent of W . In ....
O. E. Barndor -Nielsen, Superposition of Ornstein-Uhlenbeck Type processes. Preprint, MaPhySto Research Report No 2, University of Aarhus, Denmark. (1999)
Continuous Time Volatility Modelling: COGARCH versus.. - Klüppelberg, Lindner, .. Self-citation (Nielsen) (Correct)
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Barndor -Nielsen, O.E.: Superposition of Ornstein-Uhlenbeck type processes. Theory Probab. Appl. 45, 175-194 (2001)
Non-Gaussian OU based models and some of their uses in.. - Barndorff-Nielsen.. (2001) (1 citation) Self-citation (Barndorff-nielsen) (Correct)
....later to establish the notation that the cumulant generating functions for oe 2 (t) and z(1) if they exist) be written as k( log E Theta exp Phi Gamma oe 2 (t) Psi and k( log E [exp f Gamma z(1)g] respectively. Indeed they are related by the fundamental equality (Barndorff Nielsen (1999)) k( Z 1 0 k( e Gammas )ds; 11) which can be reexpressed as k( k 0 ( 12) where k 0 ( d k( d ) It then follows that if we write the cumulants of oe 2 (t) and z(1) when they exist) as, respectively, m and m (m = 1; 2; we have that m = ....
....and Lee (1992) Dacorogna, Muller, Olsen, and Pictet (1997) and Barndorff Nielsen (1998) 10 By choosing the weights and damping factors in (37) appropriately and letting m 1 it is possible to construct tractable volatility models with long range or quasi long range dependence. In particular, Barndorff Nielsen (1999) shows there exists a limiting model for which r(u) 1 juj) Gamma2(1 GammaH ) with 0 and H 2 ( 1 2 ; 1) being the long memory parameter. It is possible to extend this to multifractal behaviour where r(u) m X i=1 w i (1 i juj) Gamma2(1 GammaH i ) H i 2 1 2 ; 1 ; ....
Barndorff-Nielsen, O. E. (1999). Superposition of Ornstein-Uhlenbeck type processes. Unpublished paper: Department of Mathematics, Aarhus University.
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