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Partial Smoothing of the Stochastic Wave Equation and Regularization by Noise Phenomena

Author

Listed:
  • Federica Masiero

    (Università di Milano-Bicocca)

  • Enrico Priola

    (Università di Pavia)

Abstract

We establish partial smoothing properties of the transition semigroup $$(P_t)$$ ( P t ) associated to the linear stochastic wave equation driven by a cylindrical Wiener noise on a separable Hilbert space. These new results allow the study of related vector-valued infinite-dimensional PDEs in spaces of functions which are Hölder continuous along special directions. As an application we prove strong uniqueness for semilinear stochastic wave equations involving nonlinearities of Hölder type. We stress that we are able to prove well-posedness although the Markov semigroup $$(P_t)$$ ( P t ) is not strong Feller.

Suggested Citation

  • Federica Masiero & Enrico Priola, 2024. "Partial Smoothing of the Stochastic Wave Equation and Regularization by Noise Phenomena," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2738-2774, September.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:3:d:10.1007_s10959-024-01337-1
    DOI: 10.1007/s10959-024-01337-1
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    References listed on IDEAS

    as
    1. G. Prato & F. Flandoli & E. Priola & M. Röckner, 2015. "Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1571-1600, December.
    2. Franco Flandoli & Francesco Russo & Giovanni Zanco, 2018. "Infinite-Dimensional Calculus Under Weak Spatial Regularity of the Processes," Journal of Theoretical Probability, Springer, vol. 31(2), pages 789-826, June.
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