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.

Masiero, F., Orrieri, C., Tessitore, G., Zanco, G. (2021). Semilinear Kolmogorov equations on the space of continuous functions via BSDEs. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 136(June 2021), 1-56 [10.1016/j.spa.2021.01.009].

Semilinear Kolmogorov equations on the space of continuous functions via BSDEs

Masiero, F;Tessitore, G;
2021

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.
Articolo in rivista - Articolo scientifico
BSDEs; Semilinear path-dependent PDEs; Stochastic calculus in infinite dimension; Stochastic control;
English
13-feb-2021
2021
136
June 2021
1
56
none
Masiero, F., Orrieri, C., Tessitore, G., Zanco, G. (2021). Semilinear Kolmogorov equations on the space of continuous functions via BSDEs. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 136(June 2021), 1-56 [10.1016/j.spa.2021.01.009].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/308584
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