Magda Peligrad

Magda Peligrad


Charles Phelps Taft Professor

French Hall


A&S Mathematical Sciences - 0025

Professional Summary

~~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 and Practice 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

Grant: #DMS-1512936 Investigators:Peligrad, Magda 08-01-2015 -07-31-2018 National Science Foundation Spectral analysis of stochastic processes and random fields Role:PI $252,210.00 Active Type:Grant Level:National

Grant: #DMS-1441641 Investigators:Buckingham, Robert; Peligrad, Magda; Wang, Yizao; Yen, Ju-Yi 07-01-2014 -06-30-2015 National Science Foundation Cincinnati Symposium on Probability Theory and Applications 2014 Role:Co-PI $20,000.00 Completed Type:Grant Level:International

Grant: #DMS-1208237 Investigators:Peligrad, Magda 08-01-2012 -07-31-2015 National Science Foundation Asymptotic Theory for Stochastic Processes via Martingale Methods Role:PI $150,292.00 Completed Level:National

Grant: #H98230-11-1-0135 Investigators:Peligrad, Magda 05-12-2011 -05-11-2013 National Security Agency Sharp Inequalities and Limit Theorems for Stochastic Processes Role:PI $73,086.00 Completed Type:Grant Level:International

Grant: #DMS-0830579 Investigators:Bryc, Wlodzimierz; Chakraborty, Ranajit; Mitro, Joanna; Peligrad, Magda 01-01-2009 -12-31-2010 National Science Foundation Cincinnati Symposium on Probability Theory and Applications 2009 Role:Collaborator $20,000.00 Completed Type:Grant Level:International

Grant: #H98230-09-1-0005 Investigators:Peligrad, Magda 11-04-2008 -11-03-2010 National Security Agency Modeling Dependence via Martingale Approximation and Limit Theorems Role:PI $52,979.00 Completed Type:Grant Level:National

Grant: #H98230-07-1-0016 Investigators:Peligrad, Magda 12-07-2006 -12-06-2008 National Security Agency Topics in Modeling the Dependence, Maximal Inequalities and Gaussian Approximation Role:PI $45,000.00 Completed Level:National

Grant: #H98230-05-1-0066/P1 Investigators:Peligrad, Magda 11-24-2004 -11-23-2006 National Security Agency Modeling the Dependence: New Techniques and Sharp Results Role:PI $42,006.00 Completed Type:Grant Level:National

Investigators:Magda Peligrad 2017 -2017 Taft Reserach Center Functional Gaussian approximation for stochastic processes Role:PI $3,800 Completed Type:Grant Level:Local

Grant: #DMS-1811373 Investigators:Peligrad, Magda 08-01-2018 -07-31-2021 National Science Foundation Limit theorems for stochastic processes and random fields via projective conditions Role:PI $157,966.00 Awarded Level:Federal

Grant: #DMS-2054598 Investigators:Peligrad, Magda 08-01-2021 -07-31-2024 National Science Foundation Asymptotic results for stochastic processes via new projective methods Role:PI $97,898.00 Awarded Level:Federal

Grant: #DMS-2413604 Investigators:Buckingham, Robert; Guo, Xiaoqin; Peligrad, Magda; Wang, Yizao; Yen, Ju-Yi 05-01-2024 -04-30-2025 National Science Foundation Conference: Cincinnati Symposium on Probability 2024 Role:Collaborator 48620.00 Active Level:Federal

Abbreviated Publications

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

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

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

Asymptotic variance of stationary reversible and normal Markov processes (with George Deligiannidis and Sergey Utev) (2015). Electronic Journal of Probability  20, 1-26

On kernel estimators of density for reversible Markov chains (with M. Longla and H. Sang)
Statistics and Probability Letters 100 (2015) 149-157

Quenched limit theorems for Fourier transform and periodogram  (with D. Barrera). Bernoulli (2016)  22 (1) 275-301.

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.

Reflexive operator algebras on Banach Spaces   (with  Florence Merlevède, and C. Peligrad) (2014); Pacific Journal of Mathematics 267 451- 464

A quenched weak invariance principle  (with  Jérôme Dedecker, and Florence Merlevède); (2014) Annales de L Institut Henri Poincaré , Probabilites and Statistique, 50 872-898

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)

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.

Law of the iterated logarithm for the periodogram  (with Christophe Cuny and Florence Merlevède).  (2013) Stochastic Processes and their Applications 123 4065-4089

Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples (with Florence Merlevède) (2013). Annals of Probability 41  914-960More Information

Central limit theorem for linear processes with infinite variance. (with Hailin Sang) (2013). Journal of Theoretical Probabilities. 26  222-239 More Information

Central limit theorem for triangular arrays of Non-Homogeneous Markov chains. (2012);  Probability Theory and Related Fields154 409-428

More Information

Almost sure invariance principles via martingale approximation  (with Florence Merlevède and Costel Peligrad) (2012), Stoch. Proc. Appl. 122   170-190

More Information

Some Aspects of Modeling Dependence in Copula-based Markov chains (with Martial Longla)  (2012);  J.Multiv.Anal.   111, 234–240 

More Information

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.

More Information

Asymptotic Properties of Self-Normalized Linear Processes with Long Memory (with Hailin Sang); (2012) Econometric Theory, 28, 548-569   

More Information

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. 

More Information

On the invariance principle under martingale approximation (with Costel Peligrad) (2011); Stochastics and Dynamics 11, 1-11.

More Information

Invariance principles for linear processes. Application to isotonic regression. (with Jérôme Dedecker  and  Florence Merlevède) (2011). Bernoulli 17, 88-113 

More Information

On the functional CLT via martingale approximation (with M. Gordin) (2011) Bernoulli 17, 424-440.

More Information

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.

More Information

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) Stochastic Process. Appl. 128, 1333-1346.

More Information

Central limit theorem for Fourier transform and periodogram of random fields. (with Na Zhang)  Bernoulli Volume 25, Number 1, 499-520.

Martingale approximations for random fields (with Na Zhang),Electronic Communications in Probability, Vol. 23, paper no. 28, 1-9.

New robust confidence intervals for the mean under dependence (with Martial Longla)

Quenched invariance principles for orthomartingale-like sequences (with Dalibor Volny) (2019)

Functional CLT for martingale-like nonstationary dependent structures  (with Florence Merlevède and Sergey Utev)

Universality of limiting spectral distribution under projective criteria. (with Florence Merlevède)

On the quenched CLT for stationary random fields under projective criteria (with Na Zhang and Lucas Reding)


Functional Gaussian Approximation for Dependent Structures (with F. Merlevede and Sergey Utev) (2019) Oxford Press


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. Conference. . Level:International

Magda Peligrad, Costel Peligrad (2016. ) Random fields, spectral density and empirical spectral distribution. .Random processes and time series conference., San Diego. Professional Meeting. . Level:International

Magda Peligrad and Na Zhang (2017. ) Central limit theorem for discrete double Fourier series of random fields. 1127 AMS meeting, Bloomington IN . Level:International

Magda Peligrad and Na Zhang (2017. ) On the normal approximation for random fields via martingale methods. .1127 AMS meeting, Bloomington IN. Level:International

Magda Peligrad and Na Zhang (2017. ) Central limit theorem for Fourier transform and periodogram of random fields. High Dimensional Probabilities. BIRS, Oaxaca, Mexico. Level:International

Magda Peligrad and Na Zhang (2017. ) Limit Theorems for random fields via martingale approximations .Colloquium, Universite Paris-Est Marne-la-Vallee, Paris, FranceFrance. Level:International

Magda Peligrad and Zhang Na (2017. ) On the martingale methods for random fields. .Limit Theorems for Dependent Random Variables and Applications, Rouen, France. Level:International


Nonstationary martingale methods. Cincinnati. UC. Level:Department

Honors and Awards

1995 Fellow of the Institute of Mathematical Statistics Demonstrated distinction in research in statistics or probability, by publication of independent work of merit.

1996 Faculty Achievement Award

2003 Distinguished Reserach Taft Professor

2010 CONFERENCE in honour of Professor MAGDA PELIGRAD, Paris France Status:Recipient Level:International Type:Recognition

2017 University of Cincinnati Fellow of the Graduate School Status:Recipient Level:University Type:Recognition


Institute of Mathematical Statistics (Fellows Committee ) Committee Member Type:Service to Professional Associations Level:International 2015 -2018

Annals of Statistics Peer Review/Referee Type:Editorial Service Level:International

ALEA Reviewer Type:Editorial Service Level:International

Journal of theoretical probabilities Reviewer Type:Editorial Service Level:International


Probability Theory and Stochastic Processes with a view towards applications in Statistics.