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Smooth density for the solution of scalar SDEs with locally Lipschitz coefficients under Hörmander condition

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  • Tahmasebi, M.

Abstract

In this paper the existence of a smooth density is proved for the solution of an SDE, with locally Lipschitz coefficients and semi-monotone drift, under Hörmander condition. We prove the nondegeneracy condition for the solution of the SDE, from it an integration by parts formula would result in the Wiener space. To this end we construct a sequence of SDEs with globally Lipschitz coefficients whose solutions converge to the original one and use some Lyapunov functions to show the uniform boundedness of the p-moments of the solutions and their Malliavin derivatives with respect to n.

Suggested Citation

  • Tahmasebi, M., 2014. "Smooth density for the solution of scalar SDEs with locally Lipschitz coefficients under Hörmander condition," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 51-62.
    • Handle: RePEc:eee:stapro:v:85:y:2014:i:c:p:51-62
    DOI: 10.1016/j.spl.2013.11.004
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    References listed on IDEAS

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    1. Ren, Yao-Feng, 2008. "On the Burkholder-Davis-Gundy inequalities for continuous martingales," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 3034-3039, December.
    2. Alos, Elisa & Ewald, Christian-Oliver, 2007. "Malliavin differentiability of the Heston volatility and applications to option pricing," MPRA Paper 3237, University Library of Munich, Germany.
    3. Arturo Kohatsu & Montero Miquel, 2003. "Malliavin calculus in finance," Economics Working Papers 672, Department of Economics and Business, Universitat Pompeu Fabra.
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