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Semilinear Kolmogorov equations on the space of continuous functions via BSDEs

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  • Masiero, Federica
  • Orrieri, Carlo
  • Tessitore, Gianmario
  • Zanco, Giovanni

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.

Suggested Citation

  • Masiero, Federica & Orrieri, Carlo & Tessitore, Gianmario & Zanco, Giovanni, 2021. "Semilinear Kolmogorov equations on the space of continuous functions via BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 1-56.
    • Handle: RePEc:eee:spapps:v:136:y:2021:i:c:p:1-56
    DOI: 10.1016/j.spa.2021.01.009
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    References listed on IDEAS

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    1. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    2. Guatteri, Giuseppina & Masiero, Federica & Orrieri, Carlo, 2017. "Stochastic maximum principle for SPDEs with delay," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2396-2427.
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