10 citations · 16 across the 21 of their papers we have counts for
21 papers
Investigation and Development of the Methodologies for Simulating Self-similar Processes
Qidi Peng, William Wu
This paper is devoted to the study of simulating a large class of self-similar processes. Since most current simulation approaches are limited to case-by-case studies, every existi…
On a theorem of Nikol'skii
Asuman G. Aksoy, Qidi Peng
We present Bernstein lethargy theorem and examine the relationship between Bernstein lethargy theorem and reflexivity.
Fractional Brownian Motion: Local Modulus of Continuity with Refined Almost Sure Upper Bound and First Exit Time from One-sided Barrier
Qidi Peng, Nan Rao
Based on an optimal rate wavelet series representation, we derive a local modulus of continuity result with a refined almost sure upper bound for fractional Brownian motion. \slopp…
Variable Selection and Regularization via Arbitrary Rectangle-range Generalized Elastic Net
Yujia Ding, Qidi Peng, Zhengming Song +1
We introduce the arbitrary rectangle-range generalized elastic net penalty method, abbreviated to ARGEN, for performing constrained variable selection and regularization in high-di…
Linear Multifractional Stable Sheets in the Broad Sense: Existence and Joint Continuity of Local Times
Yujia Ding, Qidi Peng, Yimin Xiao
We introduce the notion of linear multifractional stable sheets in the broad sense (LMSS) with , to include both linear multifractional Brownian sheets () and linea…
Series Representation of Jointly SS Distribution via Symmetric Covariations
Yujia Ding, Qidi Peng
We introduce the notion of symmetric covariation, which is a new measure of dependence between two components of a symmetric -stable random vector, where the stability parameter…
Some Developments in Clustering Analysis on Stochastic Processes
Qidi Peng, Nan Rao, Ran Zhao
We review some developments on clustering stochastic processes and come with the conclusion that asymptotically consistent clustering algorithms can be obtained when the processes…
Cluster Analysis on Locally Asymptotically Self-similar Processes with Known Number of Clusters
Qidi Peng, Nan Rao, Ran Zhao
We conduct cluster analysis on a class of locally asymptotically self-similar stochastic processes, which includes multifractional Brownian motion as a representative. When the tru…
Bernstein Lethargy Theorem and Reflexivity
Asuman Güven Aksoy, Qidi Peng
In this paper, we prove the equivalence of reflexive Banach spaces and those Banach spaces which satisfy the following form of Bernstein's Lethargy Theorem. Let be an arbitrary…
Covariance-based Dissimilarity Measures Applied to Clustering Wide-sense Stationary Ergodic Processes
Qidi Peng, Nan Rao, Ran Zhao
We introduce a new unsupervised learning problem: clustering wide-sense stationary ergodic stochastic processes. A covariance-based dissimilarity measure together with asymptotical…
A General Class of Multifractional Processes and Stock Price Informativeness
Qidi Peng, Ran Zhao
We introduce a general class of stochastic processes driven by a multifractional Brownian motion (mBm) and study the estimation problems of their pointwise Hölder exponents (PHE) b…
Subspace Condition for Bernstein's Lethargy Theorem
Asuman GÜven Aksoy, Monairah Al-Ansari, Caleb Case +1
In this paper, we consider a condition on subspaces in order to improve bounds given in the Bernstein's Lethargy Theorem (BLT) for Banach spaces. Let $d_1 \geq d_2 \geq \dots d_n \…
Constructing an Element of a Banach Space with Given Deviation from its Nested Subspaces
Asuman G. Aksoy, Qidi Peng
This paper contains two improvements on a theorem of S. N. Bernstein for Banach spaces. We show that if is an arbitrary infinite-dimensional Banach space, is a sequen…
A New Algorithm to Simulate the First Exit Times of a Vector of Brownian Motions, with an Application to Finance
Chiu-Yen Kao, Qidi Peng, Henry Schellhorn +1
We provide a new methodology to simulate the first exit times of a vector of Brownian motions from an orthant. This new approach can be used to simulate the first exit times of dim…
Representation Theorems of -trees and Brownian Motions Indexed by -trees
Asuman G. Aksoy, Monariah Al-Ansari, Qidi Peng
We provide a new representation of an -tree by using a special set of metric rays. We have captured the four-point condition from these metric rays and shown an equivale…
Estimation of the Pointwise Hölder Exponent of Hidden Multifractional Brownian Motion Using Wavelet Coefficients
Sixian Jin, Qidi Peng, Henry Schellhorn
We propose a wavelet-based approach to construct consistent estimators of the pointwise Hölder exponent of a multifractional Brownian motion, in the case where this underlying proc…
Fractional Hida Malliavin Derivatives and Series Representations of Fractional Conditional Expectations
Sixian Jin, Qidi Peng, Henry Schellhorn
We represent fractional conditional expectations of a functional of fractional Brownian motion as a convergent series in L^2 space. When the target random variable is some function…
A Representation Theorem for Smooth Brownian Martingales - New Example
Sixian Jin, Qidi Peng, Henry Schellhorn
We show that, under certain smoothness conditions, a Brownian martingale, when evaluated at a fixed time, can be represented via an exponential formula at a later time. The time-de…
A Bond Option Pricing Formula in the Extended CIR Model, with an Application to Stochastic Volatility
Zheng Liu, Qidi Peng, henry Schellhorn
We provide a complete representation of the interest rate in the extended CIR model. Since it was proved in Maghsoodi (1996) that the representation of the CIR process as a sum of…
Hölder regularity and series representation of a class of stochastic volatility models
Antoine Ayache, Qidi Peng
Let be an arbitrary continuously differentiable deterministic function such that is bounded by a polynomial. In this article we consider the class of…
A Representation Theorem for Smooth Brownian Martingales
Henry Schellhorn
We show that, under certain smoothness conditions, a Brownian martingale at a fixed time can be represented as an exponential of its value at a later time. The time-dependent gener…