A MAXIMAL Lp-INEQUALITY FOR STATIONARY SEQUENCES AND ITS APPLICATIONS
نویسندگان
چکیده
The paper aims to establish a new sharp Burkholder-type maximal inequality in Lp for a class of stationary sequences that includes martingale sequences, mixingales and other dependent structures. The case when the variables are bounded is also addressed, leading to an exponential inequality for a maximum of partial sums. As an application we present an invariance principle for partial sums of certain maps of Bernoulli shifts processes.
منابع مشابه
A new maximal inequality and invariance principle for stationary sequences
We derive a new maximal inequality for stationary sequences under a martingale-type condition introduced by Maxwell and Woodroofe (2000). Then, we apply it to establish the Donsker invariance principle for this class of stationary sequences. A Markov chain example is given in order to show the optimality of the conditions imposed. Short title: A New Maximal Inequality I Results Let (Xi)i∈Z be a...
متن کاملHardy-type Inequalities via Auxiliary Sequences
k=1 |ak|, in which C = (cj,k) and the parameter p are assumed fixed (p > 1), and the estimate is to hold for all complex sequences a. The lp operator norm of C is then defined as the p-th root of the smallest value of the constant U : ||C||p,p = U 1 p . Hardy’s inequality thus asserts that the Cesáro matrix operator C, given by cj,k = 1/j, k ≤ j and 0 otherwise, is bounded on lp and has norm ≤ ...
متن کاملProof of a conjecture of José L . Rubio de Francia
Given a compact connected abelian group G, its dual group Γ can be ordered (in a non-canonical way) so that it becomes an ordered group. It is known that, for any such ordering on Γ and p in the range 1 < p < ∞, the characteristic function χI of an interval I in Γ is a p−multiplier with a uniform bound (independent of I) on the corresponding operator SI on Lp(G). In this note it is shown that, ...
متن کاملWaseda International Symposium on “ Stable Process , Semimartingale , Finance & Pension Mathematics
(1) Generalized Periodogram and Its Statistical Inference for Time Series Yan Liu (Waseda Univ.) Abstract: Periodogram plays a crucial role in the parameter estimation in time series analysis. We generalize the idea of periodogram from a unified point of view of time series regression. The asymptotics for the periodogram of score function in M-estimation and the self-normalized periodogram are ...
متن کاملIndescribable cardinals without diamonds
where E is a stationary subset of some cardinal ~. Jensen (cf. I-D2]) showed that if K is regular and uncountable and V=L then O~,E holds. Following his work, a number of applications of this principle and its modifications have been developed which are wide ranging and not restricted to set theory (cf. [-D1]). Jensen had also discovered that various large cardinals carry diamond sequences with...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005