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Tensor Approximation of Generalized Correlated Diffusions and Functional Copula Operators

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  • Antonio Dalessandro
  • Gareth W. Peters

Abstract

We investigate aspects of semimartingale decompositions, approximation and the martingale representation for multidimensional correlated Markov processes. A new interpretation of the dependence among processes is given using the martingale approach. We show that it is possible to represent, in both continuous and discrete space, that a multidimensional correlated generalized diffusion is a linear combination of processes that originate from the decomposition of the starting multidimensional semimartingale. This result not only reconciles with the existing theory of diffusion approximations and decompositions, but defines the general representation of infinitesimal generators for both multidimensional generalized diffusions and as we will demonstrate also for the specification of copula density dependence structures. This new result provides immediate representation of the approximate solution for correlated stochastic differential equations. We demonstrate desirable convergence results for the proposed multidimensional semimartingales decomposition approximations.

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  • Antonio Dalessandro & Gareth W. Peters, 2015. "Tensor Approximation of Generalized Correlated Diffusions and Functional Copula Operators," Papers 1502.06349, arXiv.org.
    • Handle: RePEc:arx:papers:1502.06349
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    References listed on IDEAS

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    1. Wu, Shaomin, 2014. "Construction of asymmetric copulas and its application in two-dimensional reliability modelling," European Journal of Operational Research, Elsevier, vol. 238(2), pages 476-485.
    2. Fang, Hong-Bin & Fang, Kai-Tai & Kotz, Samuel, 2002. "The Meta-elliptical Distributions with Given Marginals," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 1-16, July.
    3. Marco Scarsini, 1984. "On measures of concordance," Post-Print hal-00542380, HAL.
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