Abstract:
Let ξ(x) be a random function of x∈Rk and
ωrp(δ,ξ)=supx,h∈Rk|h|⩽δE1/p|r∑l=0(−1)lClrξ(x+lh)|p.
Properties of ωrp(δ,ξ) as a function of δ are investigated; a number of inequalities are
obtained.
Citation:
I. A. Ibragimov, “On smoothness conditions for trajectories of random functions”, Teor. Veroyatnost. i Primenen., 28:2 (1983), 229–250; Theory Probab. Appl., 28:2 (1984), 240–262
\Bibitem{Ibr83}
\by I.~A.~Ibragimov
\paper On smoothness conditions for trajectories of random functions
\jour Teor. Veroyatnost. i Primenen.
\yr 1983
\vol 28
\issue 2
\pages 229--250
\mathnet{http://mi.mathnet.ru/tvp2292}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=700208}
\zmath{https://zbmath.org/?q=an:0533.60046|0516.60049}
\transl
\jour Theory Probab. Appl.
\yr 1984
\vol 28
\issue 2
\pages 240--262
\crossref{https://doi.org/10.1137/1128023}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1984SS85900003}
Linking options:
https://www.mathnet.ru/eng/tvp2292
https://www.mathnet.ru/eng/tvp/v28/i2/p229
This publication is cited in the following 16 articles:
A. A. Borovkov, Al. V. Bulinski, A. M. Vershik, D. Zaporozhets, A. S. Holevo, A. N. Shiryaev, “Ildar Abdullovich Ibragimov (on his ninetieth birthday)”, Russian Math. Surveys, 78:3 (2023), 573–583
Alexandre Pannier, “Pathwise large deviations for white noise chaos expansions”, Bernoulli, 28:3 (2022)
Alexander A. Gushchin, Uwe Küchler, “On estimation of delay location”, Stat Inference Stoch Process, 14:3 (2011), 273
Peter M. Kotelenez, Thomas G. Kurtz, “Macroscopic limits for stochastic partial differential equations of McKean–Vlasov type”, Probab. Theory Relat. Fields, 146:1-2 (2010)
Amarjit Budhiraja, Paul Dupuis, Vasileios Maroulas, “Large deviations for infinite dimensional stochastic dynamical systems”, Ann. Probab., 36:4 (2008)
M. Ya. Kelbert, N. N. Leonenko, M. D. Ruiz-Medina, “Fractional random fields associated with stochastic fractional heat equations”, Advances in Applied Probability, 37:1 (2005), 108
N. A. Kolodij, “Some properties of random fields connected with stochastic integrals with respect to strong martingales”, J. Math. Sci. (N. Y.), 137:1 (2006), 4531–4540
Jie Xiong, “A stochastic log-Laplace equation”, Ann. Probab., 32:3B (2004)
I. A. Ibragimov, “An Estimation Problem for Quasilinear Stochastic Partial Differential
Equations”, Problems Inform. Transmission, 39:1 (2003), 51–77
I. A. Ibragimov, R. Z. Khas'minskii, “Estimation problems for coefficients of stochastic partial differential equations. Part III”, Theory Probab. Appl., 45:2 (2001), 210–232
I. A. Ibragimov, R. Z. Khas'minskii, “Estimation problems for coefficients of stochastic partial differential equations. Part I”, Theory Probab. Appl., 43:3 (1999), 370–387
Peter Imkeller, “On the perturbation problem for occupation densities”, Stochastic Processes and their Applications, 49:1 (1994), 41
Kotelenez Peter, “Existence, uniqueness and smoothnessfor a class of function valued stochastic partial differential equations”, Stochastics and Stochastic Reports, 41:3 (1992), 177
Michel Ledoux, Michel Talagrand, Probability in Banach Spaces, 1991, 297
Xavier Fernique, Probability in Banach Spaces 7, 1990, 83
Peter Kotelenez, Stochastic Space—Time Models and Limit Theorems, 1985, 95
Citation in format AMSBIB
Contact us: