Ir al contenido

Documat


Integration-by-parts characterizations of Gaussian processes

  • Autores: Ehsan Azmoodeh, Tommi Sottinen, Ciprian A. Tudor Árbol académico, Lauri Viitasaari
  • Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 72, Fasc. 1, 2021, págs. 25-41
  • Idioma: inglés
  • DOI: 10.1007/s13348-019-00278-x
  • Texto completo no disponible (Saber más ...)
  • Resumen
    • The Malliavin integration-by-parts formula is a key ingredient to develop stochastic analysis on the Wiener space. In this article we show that a suitable integration-by-parts formula also characterizes a wide class of Gaussian processes, the so-called Gaussian Fredholm processes.

  • Referencias bibliográficas
    • Alòs, E., Mazet, O., Nualart, D.: Stochastic calculus with respect to Gaussian processes. Ann. Probab. 29, 766–801 (2001)
    • Barbour, A.D.: Stein’s method for diffusion approximations. Probab. Theory Relat. Fields 84, 297–322 (1990)
    • Coutin, L., Decreusefond, L.: Stein’s method for Brownian approxima- tions. Commun. Stoch. Anal. 7, 349–372 (2013)
    • Gross, L.: Abstract Wiener spaces. In: Proceedings of Fifth Berkeley Symposium, Mathematics of Statistics and Probability, Vol. II: Contributions...
    • Hsu, E.P.: Characterization of Brownian motion on manifolds through integration by parts, in Stein’s method and applications. In: Volume 5...
    • Kuo, H.-H., Lee, Y.-J.: Integration by parts formula and the Stein lemma on abstract Wiener space. Commun. Stoch. Anal. 5, 405–418 (2011)
    • Nourdin, I., Peccati, G.: Normal Approximations with Malliavin Calculus: From Stein’s Method to Universality. Cambridge Tracts in Mathematics,...
    • Nualart, D.: The Malliavin Calculus and Related Topics, Probability and its Applications, 2nd edn. Springer, Berlin (2006)
    • Nualart, D., Nualart, E.: Introduction to Malliavin calculus. Institute of Mathematical Statistics Textbooks, vol. 9. Cambridge University...
    • Nualart, D., Saussereau, B.: Malliavin calculus for stochastioc differential equations driven by a fractional brownian motion. Stoch. Process....
    • Shih, H.-H.: On Stein’s method for infinite-dimensional Gaussian approximation in abstract Wiener spaces. J. Funct. Anal. 261, 1236–1283 (2011)
    • Sottinen, T., Viitasaari, L.: Fredholm representation of multiparameter Gaussian processes with applications to equivalence in law and series...
    • Sottinen, T., Viitasaari, L.: Stochastic analysis of Gaussian processes via Fredholm representation. Int. J. Stoch. Anal. (2016). https://doi-org.sire.ub.edu/10.1155/2016/8694365
    • Sottinen, T., Yazigi, A.: Generalized Gaussian bridges. Stoch. Process. Appl. 124, 3084–3105 (2014)
    • Sun, X., Guo, F.: On integration by parts formula and characterization of fractional Ornstein–Uhlenbeck process. Stat. Probab. Lett. 107,...
    • Üstünel, A.S.: An Introduction to Analysis on Wiener Space. Springer, New York (1995)

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno