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

    Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

    Citations

    Publications citing this paper.
    SHOWING 1-2 OF 2 CITATIONS

    Some Self‐Adjoint Quantum Semimartingales

    VIEW 3 EXCERPTS
    CITES BACKGROUND
    HIGHLY INFLUENCED

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 73 REFERENCES