Retired Research Fellow | Hwang, Chii-Ruey

**Contact Information**

- crhwang$\color{red}{@}$sinica.edu.tw
- +886 2 2368-5999 ext. 610
- +886 2 2368-9771

**Research Interests**

- Probability

**Education**

- Ph.D. in Applied Mathematics Brown University (1974-1978)
- B.S. in Mathematics National Taiwan University (1968-1972)

**Links**

**Work Experience**

- Advisory Committee on Mathematics, NSC, Taiwan, 1993-1995 2011-2013
- Member Advisory Committee on Mathematics, NSC, Taiwan 2011-2013
- Council Member The Mathematical Society of Taiwan 2008 -
- Editor Board Sankhya 2006 -
- Committee Member Assessment and Evaluation of Universities, Ministry of Education, Taiwan 2005/3 - 2005-9
- Director Mathematics Research Promotion Center, NSC, Taiwan 2002 - 2004
- Council Member Bernoulli Society 2001 -2005
- Associate Editor Statistica Sinica 1999-2002
- President The Probability and Mathematical Statistics Society,Taiwan 1998 - 2001
- Chairman EAPRC, Bernoulli Society 1997 - 2001
- Member Committee for the Revival of the East Asian and Pacific Regional Committee, Bernoulli Society 1995 - 1997
- Director Institute of Mathematics, Academia Sinica 1993-1996
- Member Advisory Committee on Mathematics, NSC, Taiwan 1993 - 1995
- Council Member The Probability and Mathematical Statistics Society,Taiwan 1992 -2010
- Council Member The Mathematical Society of Taiwan 1991 - 1999
- Deputy Director Institute of Mathematics, Academia Sinica 1987-1993
- Editor Board Soochow Journal of Mathematics 1986-2007
- Editor Board Bulletin of the Institute of Mathematics, Academia Sinica 1985-2005
- Research Fellow Institute of Mathematics, Academia Sinica 1982-
- Associate Research Fellow Institute of Mathematics, Academia Sinica 1979-1982
- Research Associate Division of Applied Mathematics, Brown University 1978-1979
- Committee Member Various International Conferences
- Committee Member Various Committees in Academia Sinica

**Research Descriptions**

Dr. Hwang's research interest is Probability theory. He investigates stochastic system with Markovian structure or arisen from real life applications. Accelerating convergence of Markov processes by anti-symmetric perturbations to a common underlying equilibrium, variance reduction in calculation of expectations, optimal updating schemes are among the main topics. The analysis of the spectral gap of anti-symmetric perturbations of Laplacian and a probabilistic approach for

the convergence rate of non-reversible processes are some of the related problems. The empirical invariances from the stock market as well as the corresponding stochastic structures are also his interests.

**Selected Publications**

- (with Lu-Jing Huang, Yin-Ting Liao, Lo-Bin Chang) "The smallest eigenvalues of random kernel matrices: asymptotic results on the min kernel"
,
*Statistics and Probability Letters*, 148, 23-29, 2019-5. - (with Lu-Jing Huang, Yin-Ting Liao, Ting-Li Chen) "Optimal Variance Reduction for Markov Chain Monte Carlo"
,
*SIAM Journal on Control and Optimization*, 56 (4), 2977-2996, 2018. - (with Hui-Hsiung Kuo, Kimiaki Saito, Jiayu Zhai) "Near-martingale property of anticipating stochastic integration"
,
*Communications on Stochastic Analysis*, 11 (4), 490-504, 2017-12. - (with Hui-Hsiung Kuo, Kimiaki Saito, Jiayu Zhai) "A General Ito formula for adapted and instantly independent stochastic processes"
,
*Communications on Stochastic Analysis*, 10 (3), 341-362, 2016-09. - (with Ting-Li Chen,Hironori Fujisawa ,Su-Yun Huang) "On the weak convergence and Central Limit Theorem of blurring and nonblurring processes with application to robust location estimation"
,
*JOURNAL OF MULTIVARIATE ANALYSIS*, 143, 165-184, 2016-01. (http://dx.doi.org/10.1016/j.jmva.2015.09.009) - (with Raoul Normand, Sheng-Jhih Wu) "Variance reduction for diffusions"
,
*Stochastic Processes and their Applications*, 125 (9), 3522-3540, 2015-09. (doi:10.1016/j.spa.2015.03.006) - (with Wei-Kuo Chen, Hsi-Wei Hsieh, Yuan-Chun Sheu) "Disorder chaos in the spherical mean-ﬁeld model"
,
*Journal of Statistical Physics*, 160 (2), 417-429, 2015-07. (DOI 10.1007/s10955-015-1264-3) - (with Sheng-Jhih Wu, Moody T. Chu) "Attaining the optimal Gaussian diffusion acceleration"
,
*Journal of Statistical Physics*, 155 (3), 571-590, 2014-03. (DOI 10.1007/s10955-014-0963-5) - (with Fushing Hsieh, Shu-Chun Chen) "Single stock dynamics on high-frequency data: from a compressed coding perspective"
,
*PLoS ONE*, 9 (2), 2014-02. (e85018.DOI: 10.1371/journal.pone.0085018, Feb. 21 2014.) - (with F. Hsieh,S.-C. Chen) "Discovering focal regions of slightly-aggregated sparse signals"
,
*Computational Statistics*, 28 (5), 2295-2308, 2013-10. (http://link.springer.com/article/10.1007%2Fs00180-013-0407-8# DOI 10.1007/s00180-013-0407-8) - (with Ting-Li Chen) "Accelerating Reversible Markov Chains"
,
*Statistics and Probability Letters*, 83 (9), 1956-1962, 2013-09. (online May 11, 2013, http://dx.doi.org/10.1016/j.spl.2013.05.002) - (with Lo-Bin Chang, Stuart Geman, Fushing Hsieh) "Invariance in the recurrence of large returns and the validation of models of price dynamics"
,
*PHYSICAL REVIEW E*, 88 (2), 0221166-1-0221166-15, 2013-08. (DOI: 10.1103/PhysRevE.88.022116) - (with Hui-Ming Pai) "Accelerating Brownian motion on N-torus"
,
*Statistics and Probability Letters*, 83 (5), 1443-1447, 2013-05. (http://www.sciencedirect.com/science/article/pii/S0167715213000527) - (with Lo-Bin Chang, Zhidong Bai, Su-Yun Huang) "Asymptotic Error Bounds for Kernel-based Nyström low-rank approximation matrices"
,
*Journal of Multivariate Analysis*, 120, 102-119, 2013-05. - (with Lo-Bin Chang,Alok Goswami,Fushing Hsieh) "An Invariance for the Large-Sample Empirical Distribution of Waiting Time between Successive Extremes"
,
*Bulletin of the Institute of Mathematics Academia Sinica, New Series*, 8 (1), 31-48, 2013. - (with Ting-Li Chen, Wei-Kuo Chen, Hui-Ming Pai) "On the Optimal Transition Matrix for MCMC Sampling"
,
*SIAM Journal on Control and Optimization*, 50 (5), 2743-2762, 2012-10. - (with Fushing Hsieh ,Shu-Chun Chen) "Discovering stock dynamics through its multidimensional volatility-phases"
,
*Quantitative Finance*, 12 (2), 213-230, 2012-02. - (with K. B. Athreya) "Gibbs measures asymptotics"
,
*Sankhya*, 72-A, 191-207, 2010. (http://sankhya.isical.ac.in/search/72a1/final11.pdf) - (with F. Hsieh,S.-C. Chen) "Non-parametric decoding on discrete time series and its applications in bioinformatics"
,
*Statistics in Biosciences*, 2, 18-40, 2010. (http://www.springerlink.com/content/h0057rl132h7th71/) - (with Brice Franke,Hui-Ming Pai,Shuenn-Jyi Sheu) "The behavior of the spectral gap under growing drift"
,
*Transactions of AMS*, 362 (3), 1325-1350, 2010. (http://www.ams.org/journals/tran/2010-362-03/S0002-9947-09-04939-3/S0002-9947-09-04939-3.pdf) - "Empirical invariance in stock market and related problems"
,
*RIMS Kokyuroku*, 1620, 18-22, 2009-01. - (with Hsieh Fushing, Y.-C. Lan, S.-B Horng, T.-K. Lee) "Exploring and reassembling patterns in female bean weevil's cognitive processing networks, 3rd revisions"
,
*Animal Cognition*, 2009. - (with Yu-Min Yeh, Hsieh Fushing) "Information on the spatial structure of aggregative marine populations via a metric correlation curve," , 2008.
- (with Lu-Jing Huang, Yin-Ting Liao, Ting-Li Chen) "Optimal Variance Reduction for Markov Chain Monte Carlo"
,
*SIAM Journal on Control and Optimization*, 2007. - (with Fushing Hsieh, Lo-Bin Chang, Ritu Sen) "Exploring stock dynamic via hierarchical segmentation: An empirical invariance on volatile duration distribution and an on-line trading strategy, first draft" , 2007.
- "Nonreversible perturbations accelerate convergence"
,
*RIMS Kokyuruku*, 1462, 26-34, 2006. - (with Su-Yun Huang) "Kernel Fisher's Discriminant Analysis in Gaussian Reproducing Kernel Hilbert Space, manuscript" , 2006.
- (with Fushing Hsieh! Hou-Cheng Lee! Yen-Chiu Lan! Shwu-Bin Horng) "Testing and mapping non-stationarity in animal behavioral processes:A case study on an individual female beam weevil"
,
*Journal of Theoretical Biology*, 238 (4), 805-816, 2006. - (with Shu-Yin Hwang-Ma, Shuenn-Jyi Sheu) "Accelerating diffusions"
,
*Annals of Applied Probability*, 15, 1433-1444, 2005. - "Accelerating Monte Carlo Markov processes"
,
*COSMOS*, 1, 87-94, 2005. - (with Hsieh Fushing!C.-T. Wu) "Least-square and cross-entropy alternating minimization algorithm for ill-posed positive linear inverse problem with degraded noise I:Introduction and applications, manuscript" , 2005.
- "Accelerating diffusions and related problems"
,
*RIMS Kokyuruku*, 1240, 58-63, 2001. - "Hwang, C.-R., Hsieh Fushing and Wu, C.-T.," , 2001.
- (with Sheu, S.-J.) "On some quadratic perturbation of Ornstein-Uhlenbeck processes"
,
*Soochow J. of Math.*, 26, 205-244, 2000. - (with Date, A. and Sheu, S.-J..) "On the number of equilibrium states in weakly coupled random networks"
,
*Statistics and Probability Letters*, 49, 291-297, 2000. - (with Chen, C.N., Chou, C.I., Kang, J., Lee, T.K. and Li, S.P.) "Monte Carlo dynamics in global optimization."
,
*Physical Review E*, 60, 2388-2393, 1999. - (with Chang, D.-C.) ""Laguerre calculus and its applications to probability measures on Heisenberg groups. " Proceedings of SAP '98, Trends in Probability and Related Analysis, 1999, 83-102, World Scientific." , 83-102, 1999.
- (with Chang, H.-C.) ""On the average-case analysis of dynamic Monte Carlo schemes." presented in the 3rd International Conference on Monte Carlo and Quasi-Monte Carlo Method, June 22-26(1998), Claremont, California, U.S.A." , 1998.
- (with Sheu, S.-J.) "On the geometrical convergence of Gibbs sampler in $R^d$."
,
*J. Multivariate Analysis*, 66, 23-37, 1998. - "Discussion paper on Markov fields, Invited paper meeting, Topic IP14 organized by A. Frigessi, Proceedings of the 50th ISI session, Beijing, Book 4, 1995." , 1995.
- (with S.-Y. Hwang-Ma Shuenn-Jyi Sheu) "Accelerating Gaussian diffusions"
,
*Ann. Applied Probab.*, 3, 897-913, 1993. - (with A.Frigessi, Shuenn-Jyi Sheu, P. di Stefano) "Convergence rate of the Gibbs sampler, the Metropolis algorithm, and other single-site updating dynamics"
,
*J. R. Statist. Soc., B*, 55, 205-219, 1993. - (with Shuenn-Jyi Sheu) "Speed up the convergence of diffusions: the Gaussian case, Thech. Report"
,
*Institute of Math., Academia Sinica*, 1992. - (with Shuenn-Jyi Sheu) "A remark on the ergodicity of systematic sweep in stochastic relaxation"
,
*Lecture Notes in Statistics (Springer)*, 74, 199-202, 1992. - (with A. Frigessi, and L. Younes) "Optimal spectral structure of reversible stochastic matrices, Monte Carlo methods and the simulation of Markov random fields"
,
*Ann. Applied Probab.*, 2, 610-628, 1992. - (with Shuenn-Jyi Sheu) "Singular perturbed Markov chains and the exact behaviors of simulated annealing processes"
,
*J. Theoretical Probab.*, 5, 223-249, 1992. - (with Shuenn-Jyi Sheu) "On the behavior of a stochastic algorithm with annealing Tech. Report"
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*Institute of Math. Academia Sinica*, 1990. - (with Shuenn-Jyi Sheu) "Large-time behavior of perturbed diffusion Markov processes with applications to the second eigenvalue problem for Fokker-Planck operators and simulated annealing"
,
*Acta Applicandae Mathematicae*, 19, 253-295, 1990. - "Random perturbation and its application to simulated annealing"
,
*Springer Verlag Lecture Notes in Physics*, 355, 165-174, 1990. - (with Shuenn-Jyi Sheu) "On the weak reversibility condition in simulated annealing"
,
*Soochow J. Math.*, 15, 159-170, 1989. - (with Shuenn-Jyi Sheu) "Remarks on Gibbs sampler and Metropolis sampler"
,
*TR Institute of Math. Academia Sinica*, 1989. - "Book Review "Simulated Annealing: Theory and Applications" by P. J. M. van Laarhoven and E. H. L. AArts (1987, Reidel, Dordrecht)"
,
*Acta Applicandae Mathematicae*, 12, 108-111, 1988. - (with Tzuu-Shuh Chiang and Shuenn-Jyi Sheu) "Diffusion for global optimization in $R^{n}$"
,
*SIAM J. Control Optim.*, 25, 737-753, 1987. - (with Shuenn-Jyi Sheu) "A generalization of Chernoff inequality via stochastic analysis75(1987), 149-157."
,
*Probability Theory and Related Fields*, 75, 149-157, 1987. - (with Shuenn-Jyi Sheu) "Application to simulated annealing, 1986." , 1986.
- (with Shuenn-Jyi Sheu) "The asymptotic behavior of the second eigenvalues of perturbed Fokker-Planck operators, 1986." , 1986.
- "Large time behaviors for perturbed diffusion Markov processes with applications I: Large time behaviors and the convergence rate to the invariant measures, TR Institute of Math. Academia Sinica, 1986."
,
*Shuenn-Jyi Sheu*, 1986. - (with Shuenn-Jyi Sheu) "Cramer's theorem for certain ergodic processes in Banach space"
,
*Stochastics*, 18, 83-94, 1986. - "A brief survey on the spectral radius and the spectral distribution of large random matrices with i.i.d. entries"
,
*Contemporary Mathematics*, 50, 145-152, 1986. - (with S. Geman) "Diffusions for global optimization"
,
*SIAM Journal of Control and Optimization*, 24, 1031-1043, 1986. - (with S. Geman) "Working paper no. 1 on diffusion with annealing, Tech. Report, Institute of Math. Academic Sinica, 1984." , 1984.
- (with Tzuu-Shuh Chiang) "On the non-uniqueness of the limit points of diffusions with a small parameter"
,
*Stochastics*, 10, 149-153, 1983. - (with Tzuu-Shuh Chiang!T.-F. Lin) "Asymptotic porbabilities of open sets of weakly convergent Gaussian measures" , 1982.
- (with Tzuu-Shuh Chiang!T.-F. Lin) "Limits of eigenvalues and eigenspaces of covariance operators of weakly convergent Gaussian measures, Tech. Report, Institute of Math. Academia Sinica 1982." , 1982.
- "Conditioning by < EQUAL, LINEAR >"
,
*Transactions of the American Mathematical Society*, 274, 69-83, 1982. - (with Stuart Geman) "A chaos hypothesis for some large systems of random equations"
,
*Z. Wahrsch. Verw. Gebiete*, 60, 291-314, 1982. - (with Stuart Geman) "Nonparametric maximum liklihood estimation by the method of sieves"
,
*Annals of Statistics*, 10, 340-356, 1982. - "A note on an invariant property of linear global constraint, Tech. Report, Institute of Math. Academia Sinica 1981." , 1981.
- "Limit problem for some linear global constraint, Tech. Report, Institute of Math. Academic Sinica 1981." , 1981.
- "A generalization of Laplace's method"
,
*Proceedings of the American Mathematical Society*, 82, 446-451, 1981. - "Working paper on Gaussian random splines, Tech. Report, Institute of Math. Academia Sinica 1980." , 1980.
- "Laplace's method revisited: Weak convergence of probability measures"
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*Annals of Probability*, 8, 1177-1182, 1980. - "Gaussian measure of large balls in a Hilbert space"
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*Proceedings of the American Mathematical Society*, 78, 107-110, 1980. - "On the 2nd limit problem in metric pattern theory II, Tech. Report, Institute of Math. Academia Sinica 1980." , 1980.
- "On the 2nd limit problem in metric pattern theory I, Tech. Report, Institute of Math. Academic Sinica 1979." , 1979.
- "A short note on Gaussian measure of small balls in a Hilbert space, Technical report, Institute of Math. Academia Sinica 1979." , 1979.

Director & Deputy Director