RESEARCH: Probability

The research of the faculty covers a broad area of probability theory, mathematical statistics, and their applications.



FACULTY

  1. Alexander, Kenneth: Probability models in statistical mechanics: lattice models (Ising model, Potts model, percolation, etc.), phase transitions, disordered models.
  2. Arratia, Richard: Probability, especially as related to combinatorics and number theory, coupling, and approximation.
  3. Bartroff, Jay: Mathematical statistics, sequential analysis, and applications.
  4. Baxendale, Peter: Stochastic dynamical systems; equilibrium, stability and bifurcation for solutions of stochastic differential equations; applications to stochastic neuronal models.
  5. Fulman, Jason: Markov chains, probability on algebraic structures, random matrix theory, Stein's method.
  6. Goldstein, Larry: Distributional approximation and Stein's method, sampling schemes in epidemiology, statistical efficiency, optimal stopping.
  7. Lototsky, Sergey: Stochastic partial differential equations, optimal nonlinear filtering of diffusion processes, statistical inference for continuous-time processes.
  8. Ma, Jin: Stochastic analysis, stochastic differential equations, stochastic control theory, mathematical finance and insurance.
  9. Mikulevicius, Remigijus (Remi): Stochastic differential equations, stochastic analysis.
  10. Minsker, Stanislav (Stas): Statistical learning theory, non-parametric statistics, concentration inequalities, mathematical finance.
  11. Piterbarg, Leonid [research]: Applied stochastic analysis, statistical models in physical oceanography.
  12. Schumitzky, Alan [emeritus]: Stochastic control theory, estimation theory and applications; population pharmacokinetics theory and applications; Bayesian analysis of nonlinear mixture models.
  13. Sun, Fengzhu (Department of Biological Sciences): Molecular and computational biology, probability, statistics.
  14. Waterman, Michael (Department of Biological Sciences): Molecular and computational biology, probability, statistics.
  15. Zhang, Jianfeng: Stochastic analysis, backward stochastic differential equations, stochastic numerics, and mathematical finance.
 

POST DOCS AND VISITORS

  • Tobias Johnson: Discrete probability and combinatorics: random regular graphs and their spectral properties; Stein’s method; interacting particle system.
  • Tuan Nguyen: High-dimensional statistics
  • James-Michael Leahy: Stochastic differential equations.
 

CURRENT GRADUATE STUDENTS:

  1. Michael Hankin (Bartroff)
  2. Yongjian Kang (Lv/Zhang)
  3. Chandrasekhar Karnam (Ma/Zhang)
  4. Gene Kim (Fulman)
  5. Dinh Nguyen (Fulman)
  6. Eunjung Noh (Ma)
  7. Enes Ozel (Fulman)
  8. Haining Ren (Fulman)
  9. Rentao Sun (Ma)
  10. Panagiotis Tsilifis (Ghanem/Mikulevicius)
  11. Cong Wu (Zhang)
  12. Weisheng Xie (Ma)
  13. Xiaojing Xing (Ma)
 

ACTIVITIES

 

RECENT GRADUATES, THEIR ADVISORS, AND DISSERTATIONS

      2015
    • Keller, Christian (Zhang), Pathwise Stochastic Analysis and Related Topics
    • Zhang, Tian (Ma), Optimal Investment and Reinsurance Problems and Related Non-Markovian FBSDEs With Constraints
    • Zheng, Zemin (Goldstein/Lv), High-Dimensional Latent Variable Thresholded Regression

 

      2014
    • Bessam, Diogo (Lototsky), Large Deviations Rates in a Gaussian Setting and Related Topics
    • Ekren, Ibrahim (Zhang), Path-Dependent Partial Differential Equations and Related Topics
    • Islak, Umit (Fulman), Concentration Inequalities with Couplings from Stein's Method
    • Sokolov, Grigory (Tartakovsky/Lototsky), Multi-Population Optimal Change-Point Detection
    • Zhuo, Jia (Zhang), Probabilistic Numerical Methods for Fully Nonlinear PDEs and Related Topics

 

      2013
    • Chubatiuk, Alona (Schumitzky), Nonparametric Estimation of an Unknown Probability Distribution Using Maximum Likelihood and Bayesian Approaches
    • Marinov, Radoslav (Fulman), Applications of Stein's Method on Statistics of Random Graphs
    • Pham, Triet (Zhang), Zero-Sum Stochastic Differential Games in Weak Formulation and Related Norms for Semi-Martingales
    • Pike, John (Fulman), Eigenfunctions for Random Walks on Hyperplane Arrangements
    • Song, Jinlin (Bartroff), Time-Sequential Testing for Multiple Hypotheses
    • Wang, Huanhuan (Ma), Asset Management with Incomplete Information
    • Wang, Xin (Ma), Nonlinear Expectations for Continuous Time Model with Jumps and Applications
    • Xu, Li (Lototsky), Parameter Estimate for Hyperbolic SPDE's with Stochastic Coefficients
    • Yildirim, Gokhan (Alexander), On the Depinning Transition of the Directed Polymer in a Random Environment With a Defect Line
    • Zhong, Jie (Lototsky), Second Order in Time Stochastic Evolution Equation and Wiener Chaos Approach

 

      2012
    • DeSalvo, Stephen (Arratia), Probabilistic Divide-and-Conquer - A New Methods for Exact Simulation - and Lower Bound Expansions for Random Bernoulli Matrices via Novel Integer Partitions
    • Du, Jie (Zhang), Stochastic Games on Stopping Times
    • Ghosh, Subhankar (Goldstein), Couplings for Berry-Esseen Bounds and Concentration Inequalities
    • Kaligotla, Sivaditya (Lototsky), Asymptotic Problems in Stochastic Partial Differential Equations: A Wiener Chaos Approach
    • Lin, Ning (Lototsky), Estimation of Coefficients in Stochsatic Differential Equations
    • Moers, Michael (Lototsky), Statistical Inference of Stochastic Differential Equations Driven by Gaussian Noise
    • Nibert, Joel (Baxendale), Invariant Measures of a Stochastic Predator-Prey Model
    • Xu, Shanshan (Lototsky/Wilcox), Initiative Non-Parametric Multivariate Regression Hypothesis Testing

 

      2011
    • Chen, Jianfu (Ma), Regime Switch Term Structure model with Forward-Backward Stochastic Differential Equations
    • Lin, Wei (Goldstein), Survival Analysis With Missing Data and High Dimensionality
    • Wang, Xinyang (Ma/Zhang), Dynamic Model for Limit Order Books and Optimal Liquidation Problems
    • Yun, Youngyun (Ma), Analysis of Correlated Defaults and Joint Default Probability in a Contagion Model

 

      2010
    • Liu, Wei (Lototsky), Statistical Inference for Stochastic Hyperbolic Equations
    • Zhang, Changyong (Mikulevicius), Numerical Weak Approximation of Stochastic Differential Equations Driven by Levy Processes

 

      2009
    • Knape, Mathias (Mikulevicius/Zapatero), A General Equilibrium Model for Exchange Rates and Asset Prices in an Economy Subject to Jump-Diffusion Uncertainty
    • Pehlivan, Lerna (Fulman), On Top to Random Shuffles, no Feedback Card Guessing and Fixed Points of Permutations
    • Polunchenko, Aleksey (Mikulevicius/Tartakovsky), Quickest Change Detection with Applications to Distributed Multi-Sensor Systems
    • Ross, Nathan (Fulman), Exchangeable Pairs in Stein's Method of Distributional Approximation

 

 

THE FIRST JOB OF SOME OF OUR RECENT GRADUATES

      2015
    • Christian Keller: Postdoc at University of Michigan
    • Tian Zhang: Education Management Systems
    • Zemin Zheng: Assistant Professor at Chinese University of Science and Technology

 

      2014
    • Diogo Bessam: Postdoc at PUC-RJ/IMPA (Brasil)
    • Ibrahim Ekren: Postdoc at ETH Zurich
    • Umit Islak: Postdoc at the University of Minnesota - Twin Cities
    • Grigory Sokolov: Postdoc at the SUNY Binghamton
    • Jia Zhuo: Morgan Stanley

 

      2013
    • Alona Chubatiuk: Postdoc at Children's Hospital LA
    • Triet Pham: Postdoc at Rutgers
    • John Pike: Postdoc at Cornell
    • Jinlin Song: Researcher at the Analysis Group
    • Huanhuan Wang: Capital One
    • Xin Wang: Morgan Stanley
    • Li Xu: Google
    • Gokhan Yildirim: Lecturer at USC
    • Jie Zhong: Postdoc at Ritsumeikan University (Japan)

 

      2012
    • Stephen DeSalvo: Postdoc at UCLA
    • Jie Du: Guggenheim Partners
    • Subhankar Ghosh: SAS Statistical Software
    • Sivaditya Kaligotla: Bloomberg LP
    • Ning Lin: Citigroup
    • Michael Moers: Deutsche Bank
    • Joel Nibert: Lecturer at USC

 

      2011
    • Jianfu Chen: Union Bank of California
    • Wei Lin: Postdoc at UPenn
    • Xinyang Wang: Morgan Stanley
    • Youngyun Yun: Union Bank of California

 

      2010
    • Wei Liu: American Express
    • Changyong Zhang: Postdoc at Salzburg University

 

      2009
    • Mathias Knape: Goldman Sachs
    • Lerna Pehlivan: Lecturer at York University
    • Aleksey Polunchenko: Postdoc at USC
    • Nathan Ross: Postdoc at UC Berkeley