Hölderian invariance principle for Hilbertian linear processes
نویسندگان
چکیده
منابع مشابه
Hölderian Invariance Principle for Hilbertian Linear Processes
Let (ξn)n≥1 be the polygonal partial sums processes built on the linear processes Xn = ∑ i≥0 ai( n−i), n ≥ 1, where ( i)i∈Z are i.i.d., centered random elements in some separable Hilbert space H and the ai’s are bounded linear operators H → H, with ∑i≥0‖ai‖ < ∞. We investigate functional central limit theorem for ξn in the Hölder spaces H o ρ(H) of functions x : [0, 1] → H such that ‖x(t+ h) − ...
متن کاملThe invariance principle for linear processes with applications
Let Xt be a linear process defined by [refer paper], where [refer paper] is greater than or equal to 0 is a sequence of real numbers and (ek, k = 0, plus or minus 1, plus or minus 2, ...) is a sequence of random variables. Two basic results, on the invariance principle of the partial sum process of the Xt converging to a standard Wiener process on [0,1], are presented in this paper. In the firs...
متن کاملConditional Autoregressive Hilbertian processes
When considering the problem of forecasting a continuous-time stochastic process over an entire time-interval in terms of its recent past, the notion of Autoregressive Hilbert space processes (arh) arises. This model can be seen as a generalization of the classical autoregressive processes to Hilbert space valued random variables. Its estimation presents several challenges that were addressed b...
متن کاملInvariance principle for stochastic processes with short memory
Abstract: In this paper we give simple sufficient conditions for linear type processes with short memory that imply the invariance principle. Various examples including projective criterion are considered as applications. In particular, we treat the weak invariance principle for partial sums of linear processes with short memory. We prove that whenever the partial sums of innovations satisfy th...
متن کاملInvariance principle, multifractional Gaussian processes and long-range dependence
This paper is devoted to establish an invariance principle where the limit process is a multifractional Gaussian process with a multifractional function which takes its values in (1/2,1). Some properties, such as regularity and local self-similarity of this process are studied. Moreover the limit process is compared to the multifractional Brownian motion. Résumé. Ce papier a pour but d’établir ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ESAIM: Probability and Statistics
سال: 2009
ISSN: 1292-8100,1262-3318
DOI: 10.1051/ps:2008011