Logarithmic Level Comparison for Small Deviation Probabilities
نویسندگان
چکیده
Log-level comparisons of the small deviation probabilities are studied in three different but related settings: Gaussian processes under the L 2 norm, multiple sums motivated by tensor product of Gaussian processes, and various integrated fractional Brownian motions under the sup-norm.
منابع مشابه
Evaluating the small deviation probabilities for subordinated Lévy processes
We study the small deviation problem for a class of symmetric Lévy processes, namely, subordinated Lévy processes. These processes can be represented as W ◦A, where W is a standard Brownian motion, and A is a subordinator independent of W . Under some mild general assumption, we give precise estimates (up to a constant multiple in the logarithmic scale) of the small deviation probabilities. The...
متن کاملLog-level Comparison for Small Deviation Probabilities
Log-level comparisons of the small deviation probabilities are studied in three different but related settings: Gaussian processes under the L2 norm, multiple sums motivated by tensor product of Gaussian processes, and various integrated fractional Brownian motions under the sup-norm. ∗Department of Mathematics, University of Idaho, Moscow, ID 83844-1103, [email protected]. Research partially ...
متن کاملL2-Small Deviations for Weighted Stationary Processes
We find logarithmic asymptotics of L2-small deviation probabilities for weighted stationary Gaussian processes (both for real and complex-valued) having power-type discrete or continuous spectrum. As in [12], our results are based on the spectral theory of pseudodifferential operators developed by Birman and Solomyak.
متن کاملLog-level Comparison Principle for Small Ball Probabilities
(if μ is the Lebesgue measure, the index μ will be omitted). The problem is to define the behavior of P{||X||μ ≤ ε} as ε → 0. The study of small deviation problem was initiated by Sytaya [S] and continued by many authors. The history of the problem in 20th century is described in reviews by Lifshits [Lf2] and by Li and Shao [LS]. Latest results can be found in [Lf3]. According to the well-known...
متن کاملA goal geometric programming problem (G2P2) with logarithmic deviational variables and its applications on two industrial problems
A very useful multi-objective technique is goal programming. There are many methodologies of goal programming such as weighted goal programming, min-max goal programming, and lexicographic goal programming. In this paper, weighted goal programming is reformulated as goal programming with logarithmic deviation variables. Here, a comparison of the proposed method and goal programming with weighte...
متن کامل