A characterization of subclasses of semi-selfdecomposable distributions by stochastic integral representations

2007 ◽  
Vol 77 (8) ◽  
pp. 838-842 ◽  
Author(s):  
Makoto Maejima ◽  
Manabu Miura
Keyword(s):  
Stochastic Integral ◽  
Integral Representations ◽  
Stochastic Integral Representations

Quantum stochastic integral representations of Fock space operators

Stochastics ◽  
2009 ◽  
Vol 81 (3-4) ◽  
pp. 367-384 ◽  
Author(s):  
Un Cig Ji ◽  
Nobuaki Obata
Keyword(s):  
Fock Space ◽  
Stochastic Integral ◽  
Integral Representations ◽  
Stochastic Integral Representations ◽  
Quantum Stochastic Integral

Asymptotic Distributions of the Least-Squares Estimators and Test Statistics in the Near Unit Root Model with Non-Zero Initial Value and Local Drift and Trend

1994 ◽  
Vol 10 (5) ◽  
pp. 937-966 ◽  
Author(s):  
Seiji Nabeya ◽  
Bent E. Sørensen
Keyword(s):  
Characteristic Function ◽  
Asymptotic Distribution ◽  
Unit Root ◽  
Stochastic Integral ◽  
Integral Representations ◽  
Characteristic Functions ◽  
General Interest ◽  
Initial Value ◽  
Stochastic Integral Representations ◽  
Near Unit Root

This paper considers the distribution of the Dickey-Fuller test in a model with non-zero initial value and drift and trend. We show how stochastic integral representations for the limiting distribution can be derived either from the local to unity approach with local drift and trend or from the continuous record asymptotic results of Sørensen [29]. We also show how the stochastic integral representations can be utilized as the basis for finding the corresponding characteristic functions via the Fredholm approach of Nabeya and Tanaka [16,17], This “link” between those two approaches may be of general interest. We further tabulate the asymptotic distribution by inverting the characteristic function. Using the same methods, we also find the characteristic function for the asymptotic distribution for the Schmidt-Phillips [26] unit root test. Our results show very clearly the dependence of the various tests on the initial value of the time series.

scholarly journals Explicit Stochastic Integral Representations for Historical Functionals

1995 ◽  
Vol 23 (4) ◽  
pp. 1772-1815 ◽  
Author(s):  
Steven N. Evans ◽  
Edwin A. Perkins
Keyword(s):  
Stochastic Integral ◽  
Integral Representations ◽  
Stochastic Integral Representations
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