Levy--Ornstein--Uhlenbeck transition semigroup as second quantized operator

• 作 者: Szymon Peszat
• 机 构: InstituteofMathematics,PolishAcademyofSciences
• 出 处: International Conference on Stochastic Partial Differential
• 发表日期: 2011年4期

　　Let \mu be an invariant measure for the transition semigroup $(P_t) $ of the Markov family defined by the Ornstein--Uhlenbeck ty pe equation d X= AXd t + d L on a Hilbert space E,driven by a Levy pro cess L.It is shown that for any t> 0,$P_t$ considered on $L^2 (\mu)$ is a second quantized operator on a Poisson Fock space of $\e ^{At}$.