RESEARCH INTERESTS
Multifractional process, statistical inferences, Malliavin calculus, stochastic differential equations, stochastic modeling, process simulation, unsupervised learning on processes, approximation theory, graph theory.
Ph.D. STUDENTS
- Nan Rao, Doctor of Philosophy, Mathematics, Claremont Graduate University.
Dissertation: Cluster Analysis on Stochastic Processes, February 2019.
- Wenjie Gao, Doctor of Philosophy, Mathematics, Claremont Graduate University.
- Yuxiao Yang, Doctor of Philosophy, Economics, Claremont Graduate University.
PUBLICATIONS
2025: Machine learning-aided lattice optimization for ultra-lightweight 3D-printed aligners , Materials & Design, with P. Narongdej, B. Yuhasz, T. Kong, D. Rojas and E. Barjasteh.
2024: Binarized l1-regularization parameters enhanced strip-wise optimization algorithm for efficient neural network optimization, IEEE Journal of Emerging and Selected Topics in Industrial Electronics, 5 (2), pp. 790 - 799, with X. Ma, P. Sun, Y. Yang, R. DeMara and Y. Bai.
2023: Fractional Brownian motion: small increments and first exit time from one-sided barrier, Chaos, Solitons & Fractals, 177 (114218), with Nan Rao.
2023: Variable selection and regularization via arbitrary rectangle-range generalized elastic net, Statistics and Computing, 33 (72), with Yujia Ding, Zhengming Song and Hansen Chen.
2023: How do demand-side incentives relate to insurance transitioning behavior of public health insurance enrollees? A novel voting ensemble approach for ranking factors of mixed data types, Quality & Quantity, with Chengcheng Zhang and Yujia Ding.
2023: Linear multifractional stable sheets in the broad sense: existence and joint continuity of local times, Bernoulli, 29 (1), pp. 785 - 814, with Yujia Ding and Yimin Xiao.
2022: BoAREN: Improving regularization in linear regression with an application to index tracking, Applied Finance Letters, 11 (1), pp. 36 - 51, with John Angus and Yujia Ding.
2022: Cluster analysis on locally asymptotically self-similar processes with known number of clusters. Fractal and Fractional, 6 (4), 222, with Nan Rao and Ran Zhao.
2021: Who determines United States healthcare out-of-pocket costs? Factor ranking and selection using ensemble learning. Health Information Science and Systems, 9 (1), 22, with Chengcheng Zhang and Yujia Ding.
2021: Series representation of jointly SaS distribution via a new type of symmetric covariations, Communications in Mathematics and Statistics, 9 (2), pp. 203 - 238, with Yujia Ding.
2020: A distributed mode reassignment scheme for mobile multihop wireless network of FDD nodes, IEEE Transactions on Aerospace and Electronic Systems, 56 (5), pp. 3599 - 3612, with Moein Parsinia, Btissam El Khamlichi and Sunil Kumar.
2019: American option pricing with regression: convergence analysis, International Journal of Theoretical and Applied Finance, 22 (8), pp. 1950044, with Chen Liu and Henry Schellhorn.
2019: Distributed mode selection for FDD communication in multihop wireless networks, IEEE Transactions on Aerospace and Electronic Systems, 55 (6), pp. 2921 - 2937, with Moein Parsinia and Sunil Kumar.
2019: Covariance-based dissimilarity measures applied to clustering wide-sense stationary ergodic processes, Machine Learning, 108 (12), pp. 1259 - 1295, with Nan Rao and Ran Zhao.
2019: Representation theorems of R-trees and Brownian motions indexed by R-trees, Asian-European Journal of Mathematics, 12 (4), 19500067, with Asuman G. Aksoy and Monairah Al-Ansari.
2019: Qidi Peng, Nan Rao and Ran Zhao, Some developments in cluster analysis on stochastic processes, Biostatistics and Biometrics Open Access Journal, 9 (3), 555764.
2018: A general class of multifractional processes and stock price informativeness. Chaos, Solitons & Fractals, 115, pp. 248 - 267, with Ran Zhao. [arXiv]
2018: Almost sure approximations in Hölder norms of a general stochastic process defined by a Young integral. ALEA, Lat. Am. J. Probab. Math. Stat., 15 (2), pp. 775 - 810, with Antoine Ayache and Céline Esser.
2018: On the distribution of extended CIR model, Statistics & Probability Letters, 142, pp. 23 - 29, with Henry Schellhorn.
2018: Constructing an element of a Banach space with given deviation from its nested subspaces. Khayyam Journal of Mathematics, 4 (1), pp. 59 - 76, with Asuman G. Aksoy. [arXiv]
2018: Estimation of the pointwise Hölder exponent of hidden multifractional Brownian motion using wavelet coefficients. Statistical Inference for Stochastic Processes, 21 (1), pp. 113 - 140, with Sixian Jin and Henry Schellhorn. [arXiv: long version]
2017: Subspace condition for Bernstein's lethargy theorem. Turkish Journal of Mathematics, 41 (5), pp. 1101 - 1107, with Asuman G. Aksoy, Monairah Al-Ansari and Caleb Case.
2016: Gender assignment for directional full-duplex FDD nodes in a multihop wireless network. In: Volume 184 of the series Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, Springer, Pages 390 - 401, with Sanjutka Bhownick, Sunil Kumar, John D. Matyjas and Moein Parsinia.
2016: A representation theorem for smooth Brownian martingales. Stochastics, 88 (5), pp. 651 - 679, with Sixian Jin and Henry Schellhorn. [arXiv]
2015: Fractional Hida-Malliavin derivatives and series representations of fractional conditional expectations. Communications on Stochastic Analysis, 9 (2), pp. 213 - 238, with Sixian Jin and Henry Schellhorn. [arXiv: long version]
2015: A new algorithm to simulate the first exit times of a vector of Brownian motions, with an application to finance. Journal of Applied Probability and Statistics, 10 (2), pp. 41 - 65, with Chiu-Yen Kao, Henry Schellhorn and Lu Zhu. [arXiv]
2015: Generating random vectors using transformation with multiple roots and its applications. Applications and Applied Mathematics, 10 (1), pp. 50 - 70, with Henry Schellhorn and Lu Zhu.
2012: Uniform Hölder exponent of a stationary increments Gaussian process: estimation starting from average values. Statistics & Probability Letters, 81 (8), pp. 1326 − 1335. [Full paper]
2011: Stochastic volatility and multifractional Brownian motion. Stochastic Differential Equations and Processes. Proceedings SAAP, Springer-Verlag, Volume 7, Pages 211 − 237, with Antoine Ayache. [Full paper]
2010: On the identification of hidden pointwise Hölder exponents. Proceeding: 42ème Journées de Statistiques, Marseille, France, with Antoine Ayache.
DISSERTATION
ACCEPTED FOR PRESENTATION AT CONFERENCES
Qidi Peng and Yanyan Yang (presenter). Do sentiment and exchange rates share memories? An application of multifractional process modeling. Accepted for presentation in poster session at the 21st Dynamic Econometrics Conference, Washington DC, U.S. (2019).
Ayca Altintig (speaker), Qidi Peng, Henry Schellhorn and Lu Zhu. An empirical analysis of counterparty risk in CDS prices. Accepted for presentation at the 2014 Financial Management Association Annual Meeting, Nashville, Tennessee, U.S. (2014).