Abstract
In this paper we consider the asymptotic behaviour of the transition density for processes of jump type as the time parameter t tends to 0. We use Picard’s duality method, which allows us to obtain the lower and upper bounds of the density even for the case where the support of Lévy measure is singular. The main result is that, under certain restrictions, the density may exhibit an exponential type decrease as t → 0 according to the accessibility of the objective points by a certain Markov chain.
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Ishikawa, Y. (2003). Exponential Type Decrease of the Density for Jump Processes with Singular Lévy Measures in Small Time. In: Çapar, U., Üstünel, A.S. (eds) Stochastic Analysis and Related Topics VIII. Progress in Probability, vol 53. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8020-6_6
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DOI: https://doi.org/10.1007/978-3-0348-8020-6_6
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