X-parameters®-based closed-form expressions for evaluating power-dependent fundamental negative and positive real impedance boundaries in oscillator design

2012 ◽  
Vol 6 (8) ◽  
pp. 835 ◽  
Author(s):  
A.M. Pelaez-Perez ◽  
S. Woodington ◽  
J.I. Alonso ◽  
M. Fernandez-Barciela ◽  
P.J. Tasker
Keyword(s):  
Closed Form ◽  
Positive Real

Linear estimation of self-similar processes via Lamperti's transformation

2000 ◽  
Vol 37 (2) ◽  
pp. 429-452 ◽  
Author(s):  
Carl J. Nuzman ◽  
H. Vincent Poor
Keyword(s):  
Brownian Motion ◽  
Closed Form ◽  
Real Line ◽  
Continuous Time ◽  
Stationary Processes ◽  
Linear Estimation ◽  
Positive Real ◽  
Self Similar ◽  
Infinite Intervals ◽  
Positive Real Line

Lamperti's transformation, an isometry between self-similar and stationary processes, is used to solve some problems of linear estimation of continuous-time, self-similar processes. These problems include causal whitening and innovations representations on the positive real line, as well as prediction from certain finite and semi-infinite intervals. The method is applied to the specific case of fractional Brownian motion (FBM), yielding alternate derivations of known prediction results, along with some novel whitening and interpolation formulae. Some associated insights into the problem of discrete prediction are also explored. Closed-form expressions for the spectra and spectral factorization of the stationary processes associated with the FBM are obtained as part of this development.

scholarly journals Empirical cumulant function based parameter estimation in stable laws

2019 ◽  
Vol 22 (2) ◽  
pp. 311-338 ◽  
Author(s):  
Annika Krutto
Keyword(s):  
Closed Form ◽  
Selection Rule ◽  
Empirical Characteristic Function ◽  
Challenging Problem ◽  
Positive Real ◽  
Infinitely Divisible ◽  
Asymptotically Normal ◽  
Cumulant Function ◽  
Independent Identically Distributed ◽  
Infinite Moments

Stable distributions are a subclass of infinitely divisible distributions that form the only family of possible limiting distributions for sums of independent identically distributed random variables. A challenging problem is estimating their parameters because many have densities with no explicit form and infinite moments. To address this problem, a class of closed-form estimators, called cumulant estimators, has been introduced. Cumulant estimators are derived from the logarithm of empirical characteristic function at two arbitrary distinct positive real arguments. This paper extends cumulant estimators in two directions: (i) it is proved that they are asymptotically normal and (ii) a sample based rule for selecting the two arguments is proposed. Extensive simulations show that under the provided selection rule, the closed-form cumulant estimators generally outperform the well-known algorithmic methods.

Linear estimation of self-similar processes via Lamperti's transformation

2000 ◽  
Vol 37 (02) ◽  
pp. 429-452 ◽  
Author(s):  
Carl J. Nuzman ◽  
H. Vincent Poor
Keyword(s):  
Brownian Motion ◽  
Closed Form ◽  
Real Line ◽  
Continuous Time ◽  
Stationary Processes ◽  
Linear Estimation ◽  
Positive Real ◽  
Self Similar ◽  
Infinite Intervals ◽  
Positive Real Line

Lamperti's transformation, an isometry between self-similar and stationary processes, is used to solve some problems of linear estimation of continuous-time, self-similar processes. These problems include causal whitening and innovations representations on the positive real line, as well as prediction from certain finite and semi-infinite intervals. The method is applied to the specific case of fractional Brownian motion (FBM), yielding alternate derivations of known prediction results, along with some novel whitening and interpolation formulae. Some associated insights into the problem of discrete prediction are also explored. Closed-form expressions for the spectra and spectral factorization of the stationary processes associated with the FBM are obtained as part of this development.

scholarly journals Closed-Form Solution of a Rational Difference Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Tarek F. Ibrahim ◽  
Abdul Qadeer Khan ◽  
Burak Oğul ◽  
Dağistan Şimşek
Keyword(s):  
Difference Equation ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Real Numbers ◽  
Positive Real ◽  
Rational Difference Equation ◽  
The Difference

In this paper, we study the solution of the difference equation Ω m + 1 = Ω m − 7 q + 6 / 1 + ∏ t = 0 5 Ω m − q + 1 t − q , where the initials are positive real numbers.

Closed Form Solutions of Joint Water-Filling for Coordinated Transmission

2010 ◽  
Vol E93-B (12) ◽  
pp. 3461-3468 ◽  
Author(s):  
Bing LUO ◽  
Qimei CUI ◽  
Hui WANG ◽  
Xiaofeng TAO ◽  
Ping ZHANG
Keyword(s):  
Closed Form ◽  
Closed Form Solutions ◽  
Water Filling
Sign in / Sign up

Export Citation Format

Share Document