alpha-selfdecomposable distributions and related Ornstein-Uhlenbeck type processes

作者：Maejima Makoto^*; Ueda Yohei

来源：Stochastic Processes and Their Applications, 2010, 120(12): 2363-2389.

DOI：10.1016/j.spa.2010.08.005

• Infinitely divisible distribution
• Levy process
• Selfdecomposable distribution
• Stochastic integral representation
• Langevin type equation
• Ornstein-Uhlenbeck type process

The concept of selfdecomposability has been generalized to that of alpha-selfdecomposability, alpha is an element of R, by many authors. We first mention the existing results on he class of alpha-selfdecomposable distributions and investigate the remaining problems. We give complete characterizations by stochastic integrals with respect to Levy processes for the case 1 <= alpha < 2. The main topic of this paper is Langevin type equations and the corresponding Ornstein-Uhlenbeck type processes related to a-selfdecomposable distributions.

• 出版日期2010-12