One of the original applications of the Malliavin calculus or the stochastic calculus of variations pertains to the analysis of the existence and smoothness of densities of random vectors on the Wiener space. In this short chapter we want to provide some useful criteria based on Malliavin calculus for Lévy processes to ensure the absolute continuity of probability laws with respect to Lebesgue measure. Finally, we discuss the smoothness of densities of strong solutions to stochastic differential equations driven by Lévy processes. See [35, 38] for further details. See also recent related developments in, e.g., [13, 14, 57, 82, 83, 137].
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© 2009 Springer-Verlag Berlin Heidelberg
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(2009). Absolute Continuity of Probability Laws. In: Nunno, G.D., Øksendal, B., Proske, F. (eds) Malliavin Calculus for Lévy Processes with Applications to Finance. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78572-9_18
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DOI: https://doi.org/10.1007/978-3-540-78572-9_18
Publisher Name: Springer, Berlin, Heidelberg
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