# Magda Peligrad

## Charles Phelps Taft Professor

### French Hall

5418

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.

## Education

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

## 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 ** 914-960

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