α-selfdecomposable distributions and related Ornstein–Uhlenbeck type processes
- Maejima, Makoto
- Ueda, Yohei
DOIAbstract
AbstractThe concept of selfdecomposability has been generalized to that of α-selfdecomposability, α∈R, by many authors. We first mention the existing results on the class of α-selfdecomposable distributions and investigate the remaining problems. We give complete characterizations by stochastic integrals with respect to Lévy processes for the case 1≤α<2. The main topic of this paper is Langevin type equations and the corresponding Ornstein–Uhlenbeck type processes related to α-selfdecomposable distributions
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