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Tytuł artykułu

Large deviations for generalized conditioned Gaussian Processes and their Bridges

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the asymptotic behavior of a Gaussian process conditioned to n linear functionals of its paths and of the bridge of such a process. In particular, functional large deviation results are stated for small time. Two examples are considered.
Rocznik
Strony
159--181
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
  • Dept. of Mathematics, University “Tor Vergata”, via della Ricerca Scientifica, 00133 Roma, Italy
Bibliografia
  • [1] P. Baldi and L. Caramellino, Asymptotics of hitting probabilities for general one-dimensional diffusions, Ann. Appl. Probab. 12 (3) (2002), pp. 1071-1095.
  • [2] L. Caramellino and B. Pacchiarotti, Large deviation estimates of the crossing probability for pinned Gaussian processes, Adv. in Appl. Probab. 40 (2008), pp. 424-453.
  • [3] L. Caramellino, B. Pacchiarotti, and S. Salvadei, Large deviation approaches for the numerical computation of the hitting probability for Gaussian processes, Methodol. Comput. Appl. Probab. 17 (2) (2015), pp. 383-401.
  • [4] A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, second edition, Springer, New York 1998.
  • [5] J.-D. Deuschel and D. W. Stroock, Large Deviations, Academic Press, Boston 1989.
  • [6] F. Giorgi and B. Pacchiarotti, Large deviations for conditional Volterra processes, Stoch. Anal. Appl. 35 (2) (2017), pp. 191-210.
  • [7] S. T. Huang and S. Cambanis, Stochastic and multiple Wiener integrals for Gaussian processes, Ann. Probab. 6 (1978), pp. 585-614.
  • [8] C. Macci and B. Pacchiarotti, Exponential tightness for Gaussian processes, with applications to some sequences of weighted means, Stochastics 89 (2) (2017), pp. 469-484.
  • [9] I. Norros, E. Valkeila, and J. Virtamo, An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions, Bernoulli 5 (4) (1999), pp. 571-587.
  • [10] D. Nualart and A. Răşcanu, Differential equations driven by fractional Brownian motion, Collect. Math. 53 (2002), pp. 55-81.
  • [11] T. Sottinen and A. Yazigi, Generalized Gaussian bridges, Stochastic Process. Appl. 124 (2014), pp. 3084-3105.
  • [12] M. Zähle, Integration with respect to fractal functions and stochastic calculus. I, Probab. Theory Related Fields 111 (1998), pp. 333-372.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9ae20c30-0ff9-45f8-bfde-e7ee052dadc9
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