Corpus ID: 124259187

# The poisson process in quantum stochastic calculus

@inproceedings{Pathmanathan2002ThePP,
title={The poisson process in quantum stochastic calculus},
author={Shayanthan Pathmanathan},
year={2002}
}
• Shayanthan Pathmanathan
• Published 2002
• Mathematics
• 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} \mathcal… CONTINUE READING

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## Quantum Wiener chaos

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