On distribution of the norm of deviation of a sub-Gaussian random process in Orlicz spaces
Abstract
The paper is devoted to the study of sub-Gaussian random variables and stochastic processes. Recall that along with centered Gaussian random variables the space Sub(Ω) of sub-Gaussian random variables contains all bounded zero-mean random variables and all zero-mean random variables whose distribution tails decrease no slower than the tails of the distribution of a Gaussian random variable. Here we study a square deviation of a sub-Gaussian random process from a constant and derive an upper estimate for the exponential moment of the deviation. The obtained result allows to estimate the distribution of deviation of a sub-Gaussian random process from some measurable function in the norm of Lp(𝕋) and in the norm of Orlicz space. The paper generalizes results of [Theory Probab. Math. Statist. 58 (1999), 51–66] for the norm of a sub-Gaussian random process in Orlicz space. As an example we apply the obtained estimates to a sub-Gaussian Wiener process deviated from a linear and a square root functions.
The author gratefully thanks Dr. Y. Kozachenko who provided insight and expertise for the research.
© 2015 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- New inequalities of Gronwall type for the stochastic differential equations
- Probability measures on fractal curves (probability distributions on the Vicsek fractal)
- The restricted isometry property for random matrices with ϕ-subgaussian entries
- On the law of the solution to a stochastic heat equation with fractional noise in time
- On distribution of the norm of deviation of a sub-Gaussian random process in Orlicz spaces
- Anticipated BDSDEs driven by Lévy process with non-Lipschitz coefficients
Artikel in diesem Heft
- Frontmatter
- New inequalities of Gronwall type for the stochastic differential equations
- Probability measures on fractal curves (probability distributions on the Vicsek fractal)
- The restricted isometry property for random matrices with ϕ-subgaussian entries
- On the law of the solution to a stochastic heat equation with fractional noise in time
- On distribution of the norm of deviation of a sub-Gaussian random process in Orlicz spaces
- Anticipated BDSDEs driven by Lévy process with non-Lipschitz coefficients
