Hitting probabilities for g-gaussian random fields

• Autores: Adrián Hinojosa
• Directores de la Tesis: Marta Sanz Solé (dir. tes.)
• Lectura: En la Universitat de Barcelona ( España ) en 2022
• Idioma: inglés
• Tribunal Calificador de la Tesis: Ciprian A. Tudor (presid.), Lluis Quer i Sardanyons (secret.), Eulalia Nualart (voc.)
• Programa de doctorado: Programa de Doctorado en Matemáticas e Informática por la Universidad de Barcelona
• Materias:
  • Matemáticas
    • Probabilidad
      • Procesos estocásticos
• Enlaces
  • Tesis en acceso abierto en: TESEO
• Resumen

  • We develop criteria for hitting probabilities of Gaussian random fields with associated canonical metric given by a class of gauge functions. This yields upper and lower bounds in terms of general notions of Hausdor↵ measure and capacity, respectively.

    We apply the criteria to the solution of the following linear stochastic partial di↵erential equations: the Poisson equation driven by white noise, the heat equation driven by fractional-colored noise and the biharmonic heat equation driven by white noise.