2016/02/11 by Francesco Cordoni, Cordoni, Francesco, Luca Di Persio +3
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Mathematical Biology Tumor Growth #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1602.03851
We consider a stochastic functional delay differential equation, namely an\nequation whose evolution depends on its past history as well as on its present\nstate, driven by a pure diffusive component plus a pure jump Poisson\ncompensated measure. We lift the problem in the infinite dimensional space of\nsquare integrable Lebesgue functions in order to show that its solution is an\nL2-valued Markov process whose uniqueness can be shown under standard\nassumptions of locally Lipschitzianity and linear growth for the coefficients.\nCoupling the aforementioned equation with a standard backward differential\nequation, and deriving some ad hoc results concerning the Malliavin derivative\nfor systems with memory, we are able to derive a non--linear Feynman--Kac\nrepresentation theorem under mild assumptions of differentiability.\n