共查询到10条相似文献,搜索用时 46 毫秒
1.
We investigate properties of square-Gaussian stochastic processes. These processes are formed by quadratic forms of Gaussian processes or by limits in the mean square of quadratic forms of Gaussian processes. Special classes of these processes are determined and investigated. For processes from these classes estimates of large deviation probability are obtained. These estimates we use to estimate the probability that Gaussian vector-valued process leave some region on some interval of time. We construct asymptotic confidence regions for estimates of covariance functions of vector-valued Gaussian processes. Criterion of hypothesis testing on covariance functions of these processes is constructed. 相似文献
2.
Miguel A. Arcones 《Journal of Theoretical Probability》1995,8(4):877-903
We present some optimal conditions for the compact law of the iterated logarithm of a sequence of jointly Gaussian processes
in different situations. We also discuss the local law of the iterated logarithm for Gaussian processes indexed by arbitrary
index sets, in particular for self-similar Gaussian processes. We apply these results to obtain the law of the iterated logarithm
for compositions of Gaussian processes.
Research partially supported by NSF Grant DMS-93-02583. 相似文献
3.
V. I. Piterbarg 《Doklady Mathematics》2016,93(2):145-147
We study probabilities of large extremes of Gaussian chaos processes, that is, homogeneous functions of Gaussian vector processes. Important examples are products of Gaussian processes and quadratic forms of them. Exact asymptotic behaviors of the probabilities are found. To this aim, we use joint results of E. Hashorva, D. Korshunov and the author on Gaussian chaos, as well as a substantially modified asymptotical Double Sum Method. 相似文献
4.
Kęstutis Kubilius Dmitrij Melichov 《Methodology and Computing in Applied Probability》2016,18(3):785-804
In this paper exact confidence intervals for the Orey index of Gaussian processes are obtained using concentration inequalities for Gaussian quadratic forms and discrete observations of the underlying process. The obtained result is applied to Gaussian processes with the Orey index which not necessarily have stationary increments. 相似文献
5.
Shunsuke Ihara 《Journal of multivariate analysis》1980,10(3):319-331
We discuss the capacity of the Gaussian channel with feedback. In general it is not easy to give an explicit formula for the capacity of a Gaussian channel, unless the channel is without feedback or a white Gaussian channel. We consider the case where a constraint, given in terms of the covariance functions of the input processes, is imposed on the input processes. It is shown that the capacity of the Gaussian channel can be achieved by transmitting a Gaussian message and using additive linear feedback. 相似文献
6.
The correspondence between Gaussian stochastic processes with values in a Banach space E and cylindrical processes which are related to them is studied. It is shown that the linear prediction of an E-valued Gaussian process is an E-valued random variable as well as the spectral measure of an E-valued Gaussian stationary process is a Gaussian random measure. 相似文献
7.
In this paper we study rough differential equations driven by Gaussian rough paths from the viewpoint of Malliavin calculus. Under mild assumptions on coefficient vector fields and underlying Gaussian processes, we prove that solutions at a fixed time are smooth in the sense of Malliavin calculus. Examples of Gaussian processes include fractional Brownian motion with Hurst parameter larger than 1/4. 相似文献
8.
A. E. Mikhailov 《Journal of Mathematical Sciences》1992,61(1):1886-1889
The properties of the oscillations of Banach-valued Gaussian processes are investigated. The oscillations of several Gaussian sequences are computed. The obtained results are used for the investigation of the properties of the trajectories of one-dimensional Gaussian processes.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 92–97, 1989. 相似文献
9.
We establish particular wavelet-based decompositions of Gaussian stationary processes in continuous time. These decompositions
have a multiscale structure, independent Gaussian random variables in high-frequency terms, and the random coefficients of
low-frequency terms approximating the Gaussian stationary process itself. They can also be viewed as extensions of the earlier
wavelet-based decompositions of Zhang and Walter (IEEE Trans. Signal Process. 42(7):1737–1745, [1994]) for stationary processes, and Meyer et al. (J. Fourier Anal. Appl. 5(5):465–494, [1999]) for fractional Brownian motion. Several examples of Gaussian random processes are considered such as the processes with
rational spectral densities. An application to simulation is presented where an associated Fast Wavelet Transform-like algorithm
plays a key role.
The second author was supported in part by the NSF grant DMS-0505628. 相似文献
10.
王亚珍 《应用数学学报(英文版)》1994,10(3):315-327
QUANTUMGAUSSIANPROCESSESWANGYAZHEN(王亚珍)(DepartmentofMathematicalStatistics,EastChinaNormalUniversity,Shanghai200062,China)Abs... 相似文献