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Anticipating linear stochastic differential equations driven by a Lévy process. (English) Zbl 1260.60108
Summary: We study the existence of a unique solution for linear stochastic differential equations driven by a Lévy process, where the initial condition and the coefficients are random and not necessarily adapted to the underlying filtration. Towards this end, we extend a method based on Girsanov transformation on Wiener space and developed by R. Buckdahn [Probab. Theory Relat. Fields 90, No. 2, 223–240 (1991; Zbl 0735.60057)] to the canonical Lévy space, which was introduced in K.-I. Sato [Lévy processes and infinitely divisible distributions. Cambridge: Cambridge University Press (1999; Zbl 0973.60001)].
MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H05 Stochastic integrals
60H07 Stochastic calculus of variations and the Malliavin calculus
60G51 Processes with independent increments; Lévy processes
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