Expertise and Current Research Activity
With modern technology, the availability of complex data in economics, engineering and other areas has improved dramatically. To handle these data one needs sophisticated mathematical models that take into account their random character due to measurement errors and unpredictability.
My research focuses on the mathematical analysis of these models with the goal of making them appropriate for applications in a variety of scientific areas. More precisely, I work on stochastic analysis, a part of probability theory that studies dynamical systems under the action of random impulses. I am the leading expert in Malliavin calculus, also called stochastic calculus of variations, which is a mathematical theory that extends the calculus of variations from functions to stochastic processes.
In the last two decades, I have developed applications of Malliavin calculus to a wide range of topics in mathematics, including regularity of probability distributions, anticipating stochastic calculus, and central limit theorems. My monograph on "The Malliavin Calculus and Its Applications" is a basic reference in this topic. Recently, I have oriented my research to time series possessing long memory and self-similarity properties. Time series with these properties are suitable models for input noises in a variety of physical phenomena including telecommunication networks, turbulence and finance.
My research activity was first developed at the University of Barcelona, where I founded a group in probability theory with high international recognition. Since I joined the University of Kansas in 2005, I have continued and expanded my research, making KU a prominent center in probability theory.
Why Study at the University of Kansas?
The Department of Mathematics at KU offers a friendly and supporting environment for the students and exceptional opportunities for learning.
Our faculty is committed to excellence in teaching and has an active research program in different areas of mathematics and its applications.
Our students have been very successful obtaining competitive positions and awards upon graduation.
Ph.D., Mathematics, University of Barcelona
Licenciado en Ciencias, Matemáticas, University of Barcelona
David Nualart works in stochastic analysis. His research interests focus on the application of Malliavin calculus to a wide range of topics including regularity of probability laws, anticipating stochastic calculus, stochastic integral representations and central limit theorems for Gaussian functionals. His recent research deals with the stochastic calculus with respect to the fractional Brownian motion and related processes. Other fields of interest are stochastic partial differential equations, rough path analysis and mathematical finance.
- Multiparameter stochastic processes
- Two-parameter martingales
- Stochastic calculus in the plane
- Markov property for random fields
- Stochastic Analysis
- Malliavin calculus
- Anticipative stochastic calculus
- Large deviationsl
- Stochastic partial differential equations
- Fractional Brownian motion
- Mathematical finance