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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2015

Flows and stochastic Taylor series in Itô calculus

Résumé

For stochastic systems driven by continuous semimartingales an explicit formula for the logarithm of the Itô flow map is given. A similar formula is also obtained for solutions of linear matrix-valued SDEs driven by arbitrary semimartingales. The computation relies on the lift to quasi-shuffle algebras of formulas involving products of Itô integrals of semimartin-gales. Whereas the Chen–Strichartz formula computing the logarithm of the Stratonovich flow map is classically expanded as a formal sum indexed by permutations, the analogous formula in Itô calculus is naturally indexed by surjections. This reflects the change of algebraic background involved in the transition between the two integration theories.
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Dates et versions

hal-01143516 , version 1 (17-04-2015)

Identifiants

Citer

Kurusch Ebrahimi-Fard, Simon J.A. Malham, Frédéric Patras, Anke Wiese. Flows and stochastic Taylor series in Itô calculus. Journal of Physics A: Mathematical and Theoretical, 2015, 48 (49), pp.495202 ⟨10.1088/1751-8113/48/49/495202⟩. ⟨hal-01143516⟩
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