Gaussian Estimates on Networks with Applications to Optimal Control

Di Persio, Luca and Ziglio, Giacomo (2011) Gaussian Estimates on Networks with Applications to Optimal Control. UNSPECIFIED. (Submitted)

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    We study a class of reaction-diffusion type equations on a finite network with continuity assumptions and a kind of non-local, stationary Kirchhoff’s conditions at the nodes. A multiplicative random Gaussian perturbation acting along the edges is also included. For such a problem we prove Gaussian estimates for the semigroup generated by the evolution operator, hence generalizing similar results previously obtained in [21]. In particular our main goal is to extend known results on Gaussian upper bounds for heat equations on networks with local boundary conditions to those with non-local ones. We conclude showing how our results can be used to apply techniques developed in [13] to solve a class of Stochastic Optimal Control Problems inspired by neurological dynamics.

    Item Type: Departmental Technical Report
    Department or Research center: Mathematics
    Subjects: Q Science > QA Mathematics > QA273 Probabilities
    Uncontrolled Keywords: Stochastic partial differential equations on networks, Gaussian estimates, Optimal stochastic control.
    Report Number: UTM 733
    Repository staff approval on: 13 Apr 2010

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