# RESEARCH: Probability

The research of the faculty covers a broad area of probability theory and its 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: Stochastic differential equations, stochastic analysis.
- Piterbarg, Leonid: Applied stochastic analysis, statistical models in physical oceanography.
- Schumitzky, Alan: Stochastic control theory, estimation theory and applications.Population pharmacokinetics theory and applications. Bayesian analysis of nonlinear mixture models.
- Tavare, Simon (Department of Biological Sciences): Statistics, computational biology, stochastic computation.
- Waterman, Michael (Department of Biological Sciences): Computational biology, probability, statistics.
- Zhang, Jianfeng: Stochastic analysis, backward stochastic differential equations, stochastic numerics, and mathematical finance.

###### Post docs and visitors:

- Tobias Johnson: Random graphs, combinatorics
- Tuan Nguyen: High dimensional data
- James Zhao: Random combinatorial structures, statistical mechanics

###### CURRENT GRADUATE STUDENTS:

- Chandrasekhar Karnam
- Christian Keller (J. Zhang)
- Gene Kim (J. Fulman)
- Haining Ren (J. Fulman)
- Panagiotis Tsilifis (J. Bartroff)
- Weisheng Xie
- Xioajing Xing (J. Ma)
- Teresa Zhang (J. Ma)
- Zemin Zheng (L. Goldstein)

###### RECENT GRADUATES:

- Knape, Mathias (Mikulevicius & Zapatero) 2009, A General Equilibrium Model for Exchange Rates and Asset Prices in an Economy Subject to Jump-Diffusion Uncertainty
- Knape, Mathias (Mikulevicius & Zapatero) 2009, A General Equilibrium Model for Exchange Rates and Asset Prices in an Economy Subject to Jump-Diffusion Uncertainty
- Polunchenko, Aleksey (P Mikulevicius & Tartakovsky) 2009, Quickest Change Detection with Applications to Distributed Multi-Sensor Systems
- Ross, Nathan (Fulman) 2009, Exchangeable Pairs in Stein's Method of Distributional Approximation
- Pehlivan, Lerna (Fulman) 2009, On top to random shuffles, no feedback card guessing and fixed points of permutations
- Liu, Wei (Lototsky) 2010, Institutional Credit Oversight, American Express, New York Statistical Inference for Stochastic Hyperbolic Equations
- Zhang, Changyong (Mikulevicius) 2010, Numerical Weak Approximation of Stochastic Differential Equations Driven by Levy Processes
- Chen, Jianfu (Ma) 2011, Quantitative Research & Development Group, Union Bank of California Regime Switch Term Structure model with Forward-Backward Stochastic Differential Equations
- Lin, Wei (Goldstein) 2011, Survival Analysis with Missing Data and High Dimensionality
- Wang, Xinyang (Ma) 2011, Dynamic Model for Limit Order Books and Optimal Liquidation Problems
- Yun, Youngyun (Ma) 2011, Analysis of Correlated Defaults and Joint Default Probability in a Contagion Model
- DeSalvo, Stephen (Arratia) 2012, Probabilistic Divide-and-Conquer - A New Methods for Exact Simulation - and Lower Bound Expansions for Random Bernoulli Matrices via Novel Integer Partitions
- Ghosh, Subhankar (Goldstein) 2012, Couplings for Berry-Esseen Bounds and Concentration Inequalities
- Kaligotla, Sivaditya (Lototsky) 2012, Asymptotic Problems in Stochastic Partial Differential Equations: A Wiener Chaos Approach
- Du, Jie (Zhang) 2012, Guggenheim Partners Stochastic Games on Stopping Times
- Lin, Ning (Lototsky) 2012, Estimation of Coefficients in Stochsatic Differential Equations
- Moers, Michael (Lototsky) 2012, Statistical Inference of Stochastic Differential Equations Driven by Gaussian Noise
- Nibert, Joel (Baxendale) 2012, Invaraint Measures of a Stochastic Predator Prey Model
- Xu, Shanshan (Lototsky/Wilcox) 2012, Initiative Non-parametric Multivariate Regression Hypothesis Testing
- Pham, Triet (Zhang) 2013, Zero-Sum Stochastic Differential Games in Weak Formulation and Related Norms for Semi-Martingales
- Song, Jinlin (Bartroff) 2013, Analysis Group Time-Sequential Testing for Multiple Hypotheses
- Wang, Huanhuan (Ma) 2013, Capital One Asset management with Incomplete Information
- Wang, Xin (Ma) 2013, Nonlinear Expectations for Continuous Time Model with Jumps and Applications
- Zhong, Jie (Lototsky) 2013, Second Order in Time Stochastic Evolution Equation and Wiener Chaos Approach
- Chubatiuk, Alona (Schumitzky) 2013, Nonparametric Estimation of an Unknown Probability Distribution Using Maximum Likelihood and Bayesian Approaches
- Marinov, Radoslav (Fulman) 2013, Applications of Stein's Method on Statistics of Random Graphs
- Pike, John (Fulman) 2013, Eigenfunctions for Random Walks on Hyperplane Arrangements
- Xu, Li (Lototsky) 2013, Parameter Estimate for Hyperbolic SPDE's with Stochastic Coefficients
- Yildirim, Gokhan (Alexander) 2013, On the Depinning Transition of the Directed Polymer in a Random Environment with a Defect line
- Bessam, Diogo (Lototsky) 2014, Large Deviations Rates in a Gaussian Setting and Related Topics
- Ekren, Ibrahim (Zhang) 2014, Path-dependent Partial Differential Equatoins and Related Topics
- Islak, Umit (Fulman) 2014, Concentration Inequalities with Couplings from Stein's Method
- Sokolov, Grigory (Tartakovsky/Lototsky) 2014, Multi-Population Optimal Change-Point Detection
- Zhuo, Jia (Zhang) 2014, Probabilistic Numerical Methods for Fully Nonlinear PDEs and Related Topics

The research of the faculty covers a broad area of probability theory and its 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: Stochastic differential equations, stochastic analysis.
- Piterbarg, Leonid: Applied stochastic analysis, statistical models in physical oceanography.
- Schumitzky, Alan: Stochastic control theory, estimation theory and applications.Population pharmacokinetics theory and applications. Bayesian analysis of nonlinear mixture models.
- Tavare, Simon (Department of Biological Sciences): Statistics, computational biology, stochastic computation.
- Waterman, Michael (Department of Biological Sciences): Computational biology, probability, statistics.
- Zhang, Jianfeng: Stochastic analysis, backward stochastic differential equations, stochastic numerics, and mathematical finance.

###### Post docs and visitors:

- Tobias Johnson: Random graphs, combinatorics
- Tuan Nguyen: High dimensional data
- James Zhao: Random combinatorial structures, statistical mechanics

###### CURRENT GRADUATE STUDENTS:

- Karnam, Chandrasekhar (Ma and Zhang)
- Keller, Christian (Zhang)
- Kim, Gene (Fulman)
- Ren, Haining (Fulman)
- Noh, Eunjung (Ma)
- Tsilifis, Panagiotis (Bartroff)
- Sun, Rentao (Ma)
- Wu, Cong (Zhang)
- Xie, Weisheng (Ma)
- Xing, Xiaojing (Ma)
- Zhang, Tian Teresa (Ma)
- Zheng, Zemin (L. Goldstein)

###### RECENT GRADUATES:

- Knape, Mathias (Mikulevicius & Zapatero) 2009, A General Equilibrium Model for Exchange Rates and Asset Prices in an Economy Subject to Jump-Diffusion Uncertainty
- Polunchenko, Aleksey (P Mikulevicius & Tartakovsky) 2009, Quickest Change Detection with Applications to Distributed Multi-Sensor Systems
- Ross, Nathan (Fulman) 2009, Exchangeable Pairs in Stein's Method of Distributional Approximation
- Pehlivan, Lerna (Fulman) 2009, On top to random shuffles, no feedback card guessing and fixed points of permutations
- Liu, Wei (Lototsky) 2010, Institutional Credit Oversight, American Express, New York Statistical Inference for Stochastic Hyperbolic Equations
- Zhang, Changyong (Mikulevicius) 2010, Numerical Weak Approximation of Stochastic Differential Equations Driven by Levy Processes
- Chen, Jianfu (Ma) 2011, Quantitative Research & Development Group, Union Bank of California Regime Switch Term Structure model with Forward-Backward Stochastic Differential Equations
- Lin, Wei (Goldstein) 2011, Survival Analysis with Missing Data and High Dimensionality
- Wang, Xinyang (Ma & Zhang) 2011, Dynamic Model for Limit Order Books and Optimal Liquidation Problems
- Yun, Youngyun (Ma) 2011, Analysis of Correlated Defaults and Joint Default Probability in a Contagion Model
- DeSalvo, Stephen (Arratia) 2012, Probabilistic Divide-and-Conquer - A New Methods for Exact Simulation - and Lower Bound Expansions for Random Bernoulli Matrices via Novel Integer Partitions
- Ghosh, Subhankar (Goldstein) 2012, Couplings for Berry-Esseen Bounds and Concentration Inequalities
- Kaligotla, Sivaditya (Lototsky) 2012, Asymptotic Problems in Stochastic Partial Differential Equations: A Wiener Chaos Approach
- Du, Jie (Zhang) 2012, Guggenheim Partners Stochastic Games on Stopping Times
- Lin, Ning (Lototsky) 2012, Estimation of Coefficients in Stochsatic Differential Equations
- Moers, Michael (Lototsky) 2012, Statistical Inference of Stochastic Differential Equations Driven by Gaussian Noise
- Nibert, Joel (Baxendale) 2012, Invaraint Measures of a Stochastic Predator Prey Model
- Xu, Shanshan (Lototsky/Wilcox) 2012, Initiative Non-parametric Multivariate Regression Hypothesis Testing
- Pham, Triet (Zhang) 2013, Zero-Sum Stochastic Differential Games in Weak Formulation and Related Norms for Semi-Martingales
- Song, Jinlin (Bartroff) 2013, Analysis Group Time-Sequential Testing for Multiple Hypotheses
- Wang, Huanhuan (Ma) 2013, Capital One Asset management with Incomplete Information
- Wang, Xin (Ma) 2013, Nonlinear Expectations for Continuous Time Model with Jumps and Applications
- Zhong, Jie (Lototsky) 2013, Second Order in Time Stochastic Evolution Equation and Wiener Chaos Approach
- Chubatiuk, Alona (Schumitzky) 2013, Nonparametric Estimation of an Unknown Probability Distribution Using Maximum Likelihood and Bayesian Approaches
- Marinov, Radoslav (Fulman) 2013, Applications of Stein's Method on Statistics of Random Graphs
- Pike, John (Fulman) 2013, Eigenfunctions for Random Walks on Hyperplane Arrangements
- Xu, Li (Lototsky) 2013, Parameter Estimate for Hyperbolic SPDE's with Stochastic Coefficients
- Yildirim, Gokhan (Alexander) 2013, On the Depinning Transition of the Directed Polymer in a Random Environment with a Defect line
- Bessam, Diogo (Lototsky) 2014, Large Deviations Rates in a Gaussian Setting and Related Topics
- Ekren, Ibrahim (Zhang) 2014, Path-dependent Partial Differential Equatoins and Related Topics
- Islak, Umit (Fulman) 2014, Concentration Inequalities with Couplings from Stein's Method
- Sokolov, Grigory (Tartakovsky/Lototsky) 2014, Multi-Population Optimal Change-Point Detection
- Zhuo, Jia (Zhang) 2014, Probabilistic Numerical Methods for Fully Nonlinear PDEs and Related Topics