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Magda Peligrad

Title: Charles Phelps Taft Professor
Office: 5418 French Hall
Tel: 513-556-4066

~~Magda Peligrad is a professor in the Department of Mathematical Sciences, whose area of expertise is Probability Theory. Her research deals with dependent structures and covers various aspects of modeling dependence, maximal inequalities and limit theorems. Some of her results have immediate applicability to Statistics of dependent data, Nonparametric statistics and  Ergodic theory, making her field of research interdisciplinary. The results of her research are the subject of over 100 papers and chapters in various books, and were presented in a large number of lectures and talks at meetings, in the United States and abroad. Her research was rewarded by numerous National Science Foundation, National Security Agency, and Taft research center grants.  In 1995 she became an elected fellow of the Institute of Mathematical Statistics; in 2003 she received the title of distinguished Taft Professor. In 2010 her contributions to Probability theory were recognized in a meeting held in her honor in Paris, France. In 2017  she became a graduate fellow of the University of Cincinnati. Magda Peligrad serves on the editorial board of the Journal of Mathematical Analysis and Applications. She is also serving on the Committee of Fellows of the Institute of Mathematical Statistics. She was a doctoral adviser for eight Ph.D. students and hosted two postdocs.


  • Ph D., Center of Statistics of the Roumanian Academy of Science., 1981.

Research Information

Research Interests

Probability Theory and Stochastic Processes, with a stress on dependent structures and their limit theorems that can be an immediately implemented in Statistics.

Research Support

  • (PI), Peligrad, Magda, Spectral analysis of stochastic processes and random fields, National Science Foundation. (DMS-1512936), $252,210.00. 08-01-2015 to 07-31-2018. Status: Active.
  • (Co-PI), Buckingham, Robert; Peligrad, Magda; Wang, Yizao; Yen, Ju-Yi, Cincinnati Symposium on Probability Theory and Applications 2014, National Science Foundation. (DMS-1441641), $20,000.00. 07-01-2014 to 06-30-2015. Status: Completed.
  • (PI), Peligrad, Magda, Asymptotic Theory for Stochastic Processes via Martingale Methods, National Science Foundation. (DMS-1208237), $150,292.00. 08-01-2012 to 07-31-2015. Status: Completed.
  • (PI), Peligrad, Magda, Sharp Inequalities and Limit Theorems for Stochastic Processes, National Security Agency. (H98230-11-1-0135), $73,086.00. 05-12-2011 to 05-11-2013. Status: Completed.
  • (Collaborator), Bryc, Wlodzimierz; Chakraborty, Ranajit; Mitro, Joanna; Peligrad, Magda, Cincinnati Symposium on Probability Theory and Applications 2009, National Science Foundation. (DMS-0830579), $20,000.00. 01-01-2009 to 12-31-2010. Status: Completed.
  • (PI), Peligrad, Magda, Modeling Dependence via Martingale Approximation and Limit Theorems, National Security Agency. (H98230-09-1-0005), $52,979.00. 11-04-2008 to 11-03-2010. Status: Completed.
  • (PI), Peligrad, Magda, Topics in Modeling the Dependence, Maximal Inequalities and Gaussian Approximation, National Security Agency. (H98230-07-1-0016), $45,000.00. 12-07-2006 to 12-06-2008. Status: Completed.
  • (PI), Peligrad, Magda, Modeling the Dependence: New Techniques and Sharp Results, National Security Agency. (H98230-05-1-0066/P1), $42,006.00. 11-24-2004 to 11-23-2006. Status: Completed.
  • (PI), Magda Peligrad, Functional Gaussian approximation for stochastic processes, Taft Reserach Center. $3,800. 2017 to 2017. Status: Completed.
  • (PI), Peligrad, Magda, Limit theorems for stochastic processes and random fields via projective conditions, National Science Foundation. (DMS-1811373), $157,966.00. 08-01-2018 to 07-31-2021. Status: Awarded.


Peer Reviewed Publications

  • Quenched Invariance Principles via Martingale Approximation (2015); in Asymptotic laws and methods in stochastics. The volume in honour of Miklos Csorgo  work. Springer in the Fields Institute Communications Series. Springer-Verlag New York 76 121-137[Link]
  • The Selfnormalized Asymptotic Results for Linear Processes  (with Hailin Sang). (2015). Asymptotic laws and methods in stochastics. The volume in honour of Miklos Csorgo  work. Fields Institute Communications Series. Springer-Verlag New York 76 43-51
  • On the invariance principle for reversible Markov chains
    (joint with  Sergey Utev), (2016)  J. Appl. Prob. 53, (2) 593-599, 
  • On the functional CLT for stationary Markov Chains started at a point (with D. Barrera, and C. Peligrad ) (2016);  Stocastic Processes and its Applications.126. (7) 1885–1900.
  • The universality of spectral limit for random matrices with martingale differences entries  (with F. Merlevede, and C. Peligrad) (2015); Random Matrices Theory and Applications 4 1-33[Link]
  • On the universality of the limiting spectral distribution for a large class of random matrices with correlated entries  (with Florence Merlevede, Marwa Banna). (2015);  Stoch.Proc. Appl.  125  2700-2726[Link]
  • Asymptotic variance of stationary reversible and normal Markov processes (with George Deligiannidis and Sergey Utev) (2015). Electronic Journal of Probability  20, 1-26[Link]
  • On kernel estimators of density for reversible Markov chains (with M. Longla and H. Sang)
    Statistics and Probability Letters 100 (2015) 149-157[Link]
  • Quenched limit theorems for Fourier transform and periodogram  (with D. Barrera). Bernoulli (2016)  22 (1) 275-301.[Link]
  • On the product of random variables and moments of sums under dependence (2016), High Dimensional Probability VII: The Cargèse Volume.  Progress in Probability. Springer Switzerland 155-172.
  • On the spectral density of the stationary processes and random fields (with M. Lifshits). (2016) Journal of Mathematical sciences 219 (5)  789-7971
  • On the empirical spectral distribution for matrices with long memory and independent rows (with F. Merlevède) (2016). Stoc. Proc. Appl. 126 (9) 2734-2760.[Link]
  • Reflexive operator algebras on Banach Spaces   (with  Florence Merlevède, and C. Peligrad) (2014); Pacific Journal of Mathematics 267 451- 464[Link]
  • A quenched weak invariance principle  (with  Jérôme Dedecker, and Florence Merlevède); (2014) Annales de L Institut Henri Poincaré , Probabilites and Statistique, 50 872-898[Link]
  • Exact Moderate and Large Deviations for Linear Processes; ) (with Hailin Sang, Yunda  Zhong and Wei Biao Wu). (2014) Statistica Sinica  24,  957-969. (plus 9 page of supplement)[Link]
  • Asymptotic properties for linear processes of functionals of reversible Markov Chains. (2013)  "High Dimensional Probability VI: the Banff volume”, Progress in Probability Springer Basel AG Vol 66, 197-212. [Link]
  • Law of the iterated logarithm for the periodogram  (with Christophe Cuny and Florence Merlevède).  (2013) Stochastic Processes and their Applications 123 4065-4089[Link]
  • Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples (with Florence Merlevède) (2013). Annals of Probability 41  914-960Link]
  • Central limit theorem for linear processes with infinite variance. (with Hailin Sang) (2013). Journal of Theoretical Probabilities. 26  222-239 Link]
  • Central limit theorem for triangular arrays of Non-Homogeneous Markov chains. (2012);  Probability Theory and Related Fields154 409-428 [Link]
  • Almost sure invariance principles via martingale approximation  (with Florence Merlevède and Costel Peligrad) (2012), Stoch. Proc. Appl. 122   170-190[Link]
  • Some Aspects of Modeling Dependence in Copula-based Markov chains (with Martial Longla)  (2012);  J.Multiv.Anal.   111, 234–240 [Link]
  • On the functional CLT for reversible Markov Chains with nonlinear growth of the variance  (with  M. Longla, and C. Peligrad) (2012). Journal of Applied Probability  49 1091-1105.[Link]
  • Asymptotic Properties of Self-Normalized Linear Processes with Long Memory (with Hailin Sang); (2012) Econometric Theory, 28, 548-569   [Link]
  • Central limit theorem started at a point for stationary processes and additive functional of reversible Markov Chains. (with C. Cuny ). (2012).  Journal of Theoretical Probabilities. 25 171-188.  [Link]
  • On the invariance principle under martingale approximation (with Costel Peligrad) (2011); Stochastics and Dynamics 11, 1-11.
  • Invariance principles for linear processes. Application to isotonic regression. (with Jérôme Dedecker  and  Florence Merlevède) (2011). Bernoulli 17, 88-113 [Link]
  • On the functional CLT via martingale approximation (with M. Gordin) (2011) Bernoulli 17, 424-440.[Link]
  • A Bernstein type inequality and moderate deviations for weakly dependent sequences (with F. Merlevede and E. Rio) (2011) Probability Theory and Related fields 151 435-474.[Link]
  • Conditional central limit theorem via martingale approximation. Dependence in probability, analysis and number theory. (2010) Kendrick Press. 295-311
  • Central limit theorem for Fourier transform of stationary processes. (with W. B. Wu) (2010) Annals of Probability 38, 2009-2022.
  • On the normal approximation for random fields via martingale methods (with Na Zhang)[Link]
  • Central limit theorem for Fourier transform and periodogram of random fields. (with Na Zhang)[Link]
  • Martingale approximations for random fields (with Na Zhang)[Link]
  • New robust confidence intervals for the mean under dependence (with Martial Longla)[Link]

Presentations & Lectures

Invited Presentations

  • Magda Peligrad, Costel Peligrad (2016). The limiting spectral distribution in terms of spectral density. Conference on Probability and Statistics in High Dimensions , CRM Barcelona Spain.
  • Magda Peligrad, Costel Peligrad (2016). Random fields, spectral density and empirical spectral distribution. Random processes and time series conference., San Diego.
  • Magda Peligrad and Na Zhang (2017). Central limit theorem for discrete double Fourier series of random fields. 1127 AMS meeting, Bloomington IN .
  • Magda Peligrad and Na Zhang (2017). On the normal approximation for random fields via martingale methods. 1127 AMS meeting, Bloomington IN.
  • Magda Peligrad and Na Zhang (2017). Central limit theorem for Fourier transform and periodogram of random fields. High Dimensional Probabilities. BIRS, Oaxaca, Mexico.
  • Magda Peligrad and Na Zhang (2017). Limit Theorems for random fields via martingale approximations Colloquium, Universite Paris-Est Marne-la-Vallee, Paris, FranceFrance.
  • Magda Peligrad and Zhang Na (2017). On the martingale methods for random fields. Limit Theorems for Dependent Random Variables and Applications, Rouen, France.


  • Nonstationary martingale methods.. Cincinnati.

Honors & Awards

  • Fellow of the Institute of Mathematical Statistics, 1995. Demonstrated distinction in research in statistics or probability, by publication of independent work of merit..
  • Faculty Achievement Award, 1996.
  • Distinguished Reserach Taft Professor , 2003.
  • CONFERENCE in honour of Professor MAGDA PELIGRAD, Paris France, 2010.
  • University of Cincinnati Fellow of the Graduate School, 2017.

Experience & Service


  • Committee Member, Institute of Mathematical Statistics Fellows Committee, 2015 to 2018
  • Peer Review/Referee, Annals of Statistics
  • Reviewer, ALEA
  • Reviewer, Journal of theoretical probabilities
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