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Weak approximations. A Malliavin calculus approach

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  • Arturo Kohatsu

Abstract

We introduce a variation of the proof for weak approximations that is suitable for studying the densities of stochastic processes which are evaluations of the flow generated by a stochastic differential equation on a random variable that maybe anticipating. Our main assumption is that the process and the initial random variable have to be smooth in the Malliavin sense. Furthermore if the inverse of the Malliavin covariance matrix associated with the process under consideration is sufficiently integrable then approximations for densities and distributions can also be achieved. We apply these ideas to the case of stochastic differential equations with boundary conditions and the composition of two diffusions.

Suggested Citation

  • Arturo Kohatsu, 1999. "Weak approximations. A Malliavin calculus approach," Economics Working Papers 358, Department of Economics and Business, Universitat Pompeu Fabra.
  • Handle: RePEc:upf:upfgen:358
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    File URL: https://econ-papers.upf.edu/papers/358.pdf
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    Keywords

    Stochastic differential equations; boundary conditions; weak approximation; numerical analysis;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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