Mathematical Finance - This is an interdisciplinary research area which has close connection and interaction with probability, statistics, engineering, optimization, control, and finance. The purpose is to use stochastic calculus, statistical inference, optimization and control to develop and analyze quantitative financial models and optimal investing strategies.
Parameter Estimation for Stochastic Systems - Many physical scenarios can be modeled by stochastic systems driven by noises with unknown parameters. The purpose of parameter estimation is to use statistical methods to derive an optimal and implementable estimator, and to study the consistency and asymptotics of the proposed estimator.
Filtering Theory and Its Applications - Filtering theory is an active and current research field with wide applications to real world problems arising in financial market, economic, communication networks, signal processing, target detection and tracking. The purpose of filtering is to find probabilistic knowledge of the past path, current state, or the future changes of the signal based on noisy observations.
Stochastic Partial Differential Equations - Stochastic partial differential equations can be used in many areas of science to model complex systems evolving over time. It is generally difficult to solve these equations analytically. It is desirable to develop numerical methods to approximate the solutions.
Stochastic Analysis - This is a research field with deep connection to classical probability, mathematical physics, ergodic theory, operator theory, and dynamical systems. It mainly focuses on the study of diffusions and the corresponding differential operators in infinite dimensional spaces by using methods from analysis and probability.
A. Service at the Department /College Level
Served on various departmental committees: Research & Grant Committee, Math Day Committee, Undergraduate Committee, Graduate Committee, Evaluation Committee and Executive Committee. Served as Faculty Marshall for the Charles E. Schmidt College of Science at the FAU Commencement on August 4, 2009.
B. Community Service
Volunteer as judge at the dispute center for several Mu Alpha Theta Math Competitions at FAU and local high schools; Volunteer for Florida Science Olympiad (FAU).
C. Professional Service
Abstract and Applied Analysis
Acta Mathematica Scientia
Acta Mathematica Sinica
Communications in Statistics: Theory and Methods
Dynamics of Continuous, Discrete and Impulse Systems
Electronic Journal of Probability
Electronic Communication in Probability
Frontiers of Mathematics in China
IMA Journal of Management Mathematics
International Journal of Stochastic Analysis
Journal of Applied Mathematics and Stochastic Analysis
Journal of computational and Applied Mathematics
Journal of Econometrics
Mathematics and Computers in Simulation
SIAM Control and Optimization
Signal Processing Letters
Statistics and Probability Letters
including a full list of publications: http://brain.math.fau.edu/Long/hlong.htm