# RESEARCH: Probability

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

FACULTY

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

- Michael Hankin (Bartroff)
- Yongjian Kang (Lv/Zhang)
- Chandrasekhar Karnam (Ma/Zhang)
- Gene Kim (Fulman)
- Dinh Nguyen (Fulman)
- Eunjung Noh (Ma)
- Enes Ozel (Fulman)
- Haining Ren (Fulman)
- Rentao Sun (Ma)
- Panagiotis Tsilifis (Ghanem/Mikulevicius)
- Cong Wu (Zhang)
- Weisheng Xie (Ma)
- Xiaojing Xing (Ma)

### ACTIVITIES

### RECENT GRADUATES, THEIR ADVISORS, AND DISSERTATIONS

- 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

- 2015

- 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

- 2014

- 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

- 2013

- 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

- 2012

- 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

- 2011

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

- 2010

- 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

- 2009

### THE FIRST JOB OF SOME OF OUR RECENT GRADUATES

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

- 2015

- 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

- 2014

- 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)

- 2013

- 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

- 2012

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

- 2011

- Wei Liu: American Express
- Changyong Zhang: Postdoc at Salzburg University

- 2010

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

- 2009