The poisson process in quantum stochastic calculus

Thesis

Given a compensated Poisson process $(X_t)_{t \geq 0}$ based on $(\Omega, \mathcal{F}, \mathbb{P})$, the Wiener-Poisson isomorphism $\mathcal{W} : \mathfrak{F}_+(L^2 (\mathbb{R}_+)) \to L^2 (\Omega, \mathcal{F}, \mathbb{P})$ is constructed. We restrict the isomorphism to $\mathfrak{F}_+(L^2 [0,1])$ and prove some novel properties of the Poisson exponentials $\mathcal{E}(f) := \mathcal{W}(e(f))$. A new proof of the result $\Lambda_t + A_t + A^{\dagger}_t = \mathcal{W}^{-1}\widehat{X_t} \mathca...

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Authors: Pathmanathan, S

• Publisher: University of Oxford;Mathematical Institute
• Publication date: 2002
• Type of award: DPhil
• Level of award: Doctoral