# RESEARCH: Applied Mathematics

The applied mathematics group at USC includes experts and scholars in a broad range of applicable mathematics and applications. This includes ordinary, functional and partial differential equations, fluid mechanics, modeling, control, and estimation, probability, statistics, cryptography, financial mathematics, and numerical methods. Several members of our group participate in a number of interdisciplinary research efforts involving scientists and engineers from a variety of areas including engineering, biology, medicine, earth sciences, economics, finance, physics, chemistry, meteorology, and materials science. Many of these collaborations involve scholars from outside of academics at local companies and government laboratories.

###### Regular Faculty

- Kenneth Alexander (Probability and Percolation Theory)
- Richard Arratia ((Probability)
- Jay Bartroff (Statistics and Probability)
- Peter Baxendale (Probability)
- Ting Chen (Dept. of Biology) (Mathematical Biology)
- Susan Friedlander (Fluid Mechanics and Partial Differential Equations)
- Larry Goldstein (Statistics)
- Sol Golomb (Combinatorics)
- Igor Kukavica (Partial Differential Equations)
- Lei Li (Mathematical Biology and Statistics)
- Sergey Lototsky (Probability and Stochastic Analysis)
- Jin Ma (Financial Mathematics and Stochastic Analysis)
- Remy Mikulevicius (Probaility and Stochastic Analysis)
- Paul Newton (Aerospace and Mechanical Engineering) (Dynamical Systems)
- Wlodek Proskurowski (Numerical Analysis)
- Gary Rosen (Estimation and Control)
- Robert Sacker (Ordinary Differential Equations)
- Alan Schumitzky (Probability and Statistics)
- Fengzhu Sun (Dept. of Biology) (Mathematical Biology)
- Simon Tavare (Dept. of Biology) (Mathematical Biology)
- Chunming Wang (Estimation and Control)
- Michael Waterman (Dept. of Biology) (Mathematical Biology)
- Jianfeng Zhang (Financial Mathematics and Stochastic Analysis)

###### Post-Doctoral Fellows

- Hong Yin (Financial Mathematics and Fluid Mechanics)
- Rongjie Lai

###### Graduate students

- Sivaditya Kaligotla (Lototsky)
- Ning Lin (Lototsky)
- Wei Liu (Lototsky)
- Gokhan Yildirim (Lototsky)
- Jinlin Song (Bartroff)
- Subhankar Ghosh (Goldstein)
- Wei Lin (Goldstein)
- Changyong Zhang (Mikulevicius)
- Minzhao Tan (Wang)

###### A Sampling of Recent Graduates and their Doctoral Thesis Titles

- Ting Wang Ph.D. 2006 (Rosen) Approximation and Parameter Estimation for a Nonlinear Reaction-Diffusion System Modeling the Metabolism and Transport of Alcohol in the Human Body.
- Asher Shamam Ph.D. 2006 (Rosen) Fully Discrete Approximation for Parameter Estimation in Abstract Parabolic Distributed Parameter Systems
- Alexander Lytvak Ph.D. 2008 (Rosen), Parameter Estimation for the Black-Scholes Model in Mathematical Finance
- Yuliya Piterbarg Ph.D. 2009 (Rosen and Schumitzky), Population Modeling and Bayesian Estimation for the Deconviolution of Blood Alcohol Concentration from Transdermal Alcohol Biosensor Data
- Karsten Stemmann Ph.D. 2006 (Lototsky) Stochastic Differential Equations Driven by Colored Noise: Chaos Expansion and Application to Interest Rate Modeling.
- Igor Cialenco Ph.D. 2007 (Lototsky) Regularity of Solution and Parameter Estimation for SPDEs with Space-Time White Noise
- Xiufang Li Ph.D. 2007 (Lototsky) New Results on Pricing Asian Options.
- Qian Song Ph.D. 2008 (Lototsky) Optimal and Exact Control of Evolution Equations
- Haiyan Huang Ph.D. 2001 (Goldstein) Bounds for the Errors in Word Count Distributional Approximations
- Alexey Polunchenko Ph.D. 2009 (Mikulevicius and Tartakovsky) Topics in Sequential Quickest Change-Point Detection
- Melissa Maisch Ph.D. 2009 (Mikulevicius and Zapatero) Optimal debt allocation using a dynamic programming approach
- Mathias Knape Ph.D. 2009 (Mikulevicius and Zapatero) A general equilibrium model for exchange rates and asset prices in an economy with jump-diffusion uncertainty
- Tatiana Tatarinova Ph.D. 2006 (Schumitzky) Bayesian Analysis of Linear and Nonlinear Mixture Models
- Vartan Akopian Ph.D. 2007 (Wang) Modeling of Earth's Ionosphere and Variational Approach for Data Assimilation
- Yan Yang Ph.D. 2008 (Wang) Covariance Modeling and Estimation for Distributed Parameter Systems and their Approximations
- Philip Seliger Ph.D. 2008 (Wang) Engineering and Design Optimization