Semilinear Kolmogorov equations on the space of continuous functions via BSDEs

Federica Masiero, Carlo Orrieri, Gianmario Tessitore and Giovanni Zanco

Stochastic Processes and their Applications, 2021, vol. 136, issue C, 1-56

Abstract: We deal with a class of semilinear parabolic PDEs on the space of continuous functions that arise, for example, as Kolmogorov equations associated to the infinite-dimensional lifting of path-dependent SDEs. We investigate existence of smooth solutions through their representation via forward–backward stochastic systems, for which we provide the necessary regularity theory. Because of the lack of smoothing properties of the parabolic operators at hand, solutions in general will only share the same regularity as the coefficients of the equation. To conclude we exhibit an application to Hamilton–Jacobi–Bellman equations associated to suitable optimal control problems.

Keywords: Semilinear path-dependent PDEs; Stochastic calculus in infinite dimension; BSDEs; Stochastic control (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spa.2021.01.009

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