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- W2949465963 abstract "We consider a stochastic functional delay differential equation, namely an equation whose evolution depends on its past history as well as on its present state, driven by a pure diffusive component plus a pure jump Poisson compensated measure. We lift the problem in the infinite dimensional space of square integrable Lebesgue functions in order to show that its solution is an $L^2-$valued Markov process whose uniqueness can be shown under standard assumptions of locally Lipschitzianity and linear growth for the coefficients. Coupling the aforementioned equation with a standard backward differential equation, and deriving some ad hoc results concerning the Malliavin derivative for systems with memory, we are able to derive a non--linear Feynman--Kac representation theorem under mild assumptions of differentiability." @default.
- W2949465963 created "2019-06-27" @default.
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- W2949465963 date "2016-02-11" @default.
- W2949465963 modified "2023-09-27" @default.
- W2949465963 title "A nonlinear Kolmogorov equation for stochastic functional delay differential equations with jumps" @default.
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