Probability - Department of Mathematics

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.
Chen, Xiaohui: High-dimensional statistics, machine learning, and optimal transport.
Dimitrov, Evgeni: Integrable probability.
Fulman, Jason: Markov chains, probability on algebraic structures, random matrix theory, Stein’s method.
Goldstein, Larry: Distributional approximation and Stein’s method, high dimensional statistics, concentration inequalities, 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.
Lv, Jinchi (Marshall School of Business): statistics, machine learning, data science, business applications, and artificial intelligence and blockchain.
Ma, Jin: Stochastic analysis, stochastic differential equations, stochastic control theory, mathematical finance and insurance.
Minsker, Stanislav (Stas): Statistical learning theory, non-parametric statistics, concentration inequalities, mathematical finance.
Sun, Fengzhu (Department of Quantitative and Computational Biology): Quantitative and computational biology, probability, statistics.
Zhang, Jianfeng: Stochastic analysis, backward stochastic differential equations, stochastic numerics, and mathematical finance.

EMERITUS FACULTY

Baxendale, Peter: Stochastic dynamical systems; equilibrium, stability, and bifurcation for solutions of stochastic differential equations; applications to stochastic neuronal models.
Mikulevicius, Remigijus (Remi): Stochastic differential equations, stochastic analysis.
Waterman, Michael (Department of Quantitative and Computational Biology): Molecular and computational biology, probability, statistics.

POST DOCS

Gao, Lan: High-Dimensional Statistics, High-Dimensional Inference, and Causal Inference.
Heilman, Steven: High-Dimensional Probability, Concentration Inequalities, Theoretical Computer Science, Random Graphs.
Rychnovsky, Mark: Random Matrix Theory, Statistical Mechanics, and Kardar Parisi Zhang Universality, as well as combinatorics and epidemiology.
Xia, Weixuan: investment decisions under incomplete preferences, exotic derivatives, cryptocurrency markets, optimal control of set-valued stochastic processes, Lévy functionals and illiquidity measures, and neural network architectures applicable in these areas.

VISITORS

Valentin Tissot-Daguette, visiting Ph.D. student from Princeton University (Host: J. Zhang).

CURRENT Ph.D. STUDENTS

Atiqah Almuzaini (Ma)
Xinze Du (Lv)
Thejani Gamage (Ma)
Cora Liang (Goldstein/Sun)
Oleksandra Lymar (Goldstein/Minsker)
Bixing Qiao (Zhang)
Gaozhan Wang (Ma/Zhang)
Bo Wu (Alexander)

CURRENT MASTERS STUDENTS:

None

CURRENT UNDERGRADUATE STUDENTS:

Sam Zhang (Heilman)

ACTIVITIES

Math Finance Colloquium
Probability and Statistics Seminar. Some of the recent lectures are available here.
Math 705 (Graduate Student Probability Seminar)

RECENT Ph.D. GRADUATES, THEIR ADVISORS, AND DISSERTATIONS

For the list of the next, and some current, jobs, of our graduates, see below. Some other success stories are here.

2023

Arslan, Aykut (Lv/Yingying Fan), High-Dimensional Rescaled Square-Root Lasso under Distributional Shift and its Robustness
Iseri, Melih (Zhang), Set Values for Mean Field Games and Set Valued PDEs
Karakus, Abdullah (Alexander), First Passage Percolation in a Correlated Environment
Paguyo, J. E. (Fulman), Limit Theorems for Three Random Discrete Structures via Stein’s Method
Tan, Ying (Ma), Stochastic Two-point Boundary Value Problem and Application in Kyle-Back Equilibrium Model
Wang, Lijia (Goldstein), Statistical Citation Network Analysis and Asymmetric Error Controls
Yao, Shunan (Minsker), New Methods For Asymmetric Classification and Robust Bayesian Inference

2022

Liu, Jinting (Goldstein/Sun), Selective Inference With Confident Directions
Pollok, Austin (Zhang), High-Frequency Kelly Criterion and Fat-Tails: Gambling with an Edge
Shah, Apoorva (Lototsky), Gaussian Free Fields and Stochastic Parabolic Equations
Tarter, Alex (Goldstein/Heilman), Dimension Reduction Techniques for Noise Stability Theorems
Vossler, Patrick (Yingying Fan/Lv), Nonparametric Ensemble Learning and Inference
Wu, Yusheng (Lototsky/Tong), Asymptotic Properties of Two Network Problems with Large Random Graphs

2021

Feng, Pengbin (Ma/Zhang), Dynamic Network Model for Systemic Risk
Gangopadhyay, Ujan (Alexander), Fluctuations of the Transverse Increments in the Two-dimensional First-passage Percolation Model
Luo, Man (Ma), Topics on Dynamic Limit Order Book and its Related Computation
Rahmani, John (Fulman), Mixing Times for the Commuting Chain
Wang, Lang (Minsker), Robust Estimation of High Dimensional Parameters
Wu, Wenqian (Ma), Topics on Set-Valued Backward Stochastic Differential Equations
Zhu, Zimu (Zhang), Some Topics on Continuous Time Principal-Agent Problem

2020

Aronowitz, Julian (Bartroff), Finite Sample Bounds in Group Sequential Analysis via Stein’s Method
Phonsom, Chukiat (Mikulevicius), On Stochastic Integro-Differential Equations
Ruan, Jie (Zhang), Numerical Methods for High-Dimensional Path-Dependent PDEs Driven by Stochastic Volterra Equations
Wei, Xiaohan (Minsker/Neely), Part I: Asynchronous optimization over weakly coupled renewal systems. Part II: High dimensional estimation under weak moment assumptions
Wu, Hao (Zhang/Lv), Statistical Insights into Deep Learning and Flexible Causal Inference

2019

Demirkaya, Emre (Yingying Fan/Goldstein/Lv), Reproducible Large-Scale Inference in High-Dimensional Nonlinear Models
He, Xinrui (Bartroff), Asymptotically optimal sequential multiple testing with (or without) prior information on the number of signals
Ozdemir, Alperen (Fulman), On Limiting Distribution and Convergence Rates of Random Processes Defined Over Discrete Structures
Wiroonsri, Nathakhun (Goldstein), Steins’ Method via Approximate Zero Biasing and Positive Association with Applications to the Combinatorial Central Limit Theorem and Statistical Physics
Xu, Fanhui (Mikulevicius), On the parabolic Kolmogorov integro-differential equation and its applications

2018

Bhattacharjee, Chinmoy (Goldstein), Stein’s Method and its Applications in Strong Embeddings and Dickman Approximations
Kim, Gene B (Fulman), Distribution of Descents in Matchings
Kim, Hyun-Jung (Lototsky), Time-Homogeneous Parabolic Anderson Model
Noh, Eunjung (Ma), Equilibrium Model of Limit Order Book and Optimal Execution Problem
Ozel, Enes (Fulman), Cycle Structures of Permutations with Restricted Positions
Sun, Rentao (Ma), Conditional Mean-Field Stochastic Differential Equations and Their Applications
Wang, Jian (Lototsky), Statistical Inference For Second-Order Ordinary Differential Equation Driven by Additive Gaussian White Noise

2017

Hankin, Michael (Bartroff), Sequential Testing of Multiple Hypotheses With FDR Control Under Dependence
Nguyen, Dinh (Fulman), Random Walks on Finite Groups and Their Irreducible Representations
Wu, Cong (Zhang), Controlled McKean-Vlasov Equations and Related Topics
Xing, Xiaojing (Ma), Optimal Investment and Dividend under Sparre Andersen Model

2016

Kang, Yongjian (Lv/Zhang), Large-Scale Inference in Multiple Gaussian Graphical Models
Karnam, Chandrasekhar (Ma/Zhang), Dynamic Approaches for some Time Inconsistent Problems
Tsilifis, Panagiotis (Ghanem/Mikulevicius), Design, Adaptation and Variational Methods in Uncertainty Quantification
Xie, Weisheng (Ma), Stochastic Differential Equations Driven by Fractional Brownian Motion and Poisson Point Processes

2015

Keller, Christian (Zhang), Pathwise Stochastic Analysis and Related Topics
Ren, Haining (Fulman), Convergence Rates of i-Cycles After an m-Shelf Shuffle
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

Daley, Timothy (Smith/Waterman), Non-Parametric Models For Large Capture-Recapture Experiments With Applications to DNA Sequencing
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 Method 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 Stochastic 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) JOBS OF SOME OF OUR RECENT Ph.D. GRADUATES