# Prof. Viens takes home a College of Science Research Award

*Prof. Frederi Viens (left) accepts a College of Science Research Award from Science dean Jeff Roberts.*

A packed lecture hall in the Lawson Computer Science Building saw Statistics and Mathematics Prof. Frederi Viens accept the College of Science's fourth Research Award of 2013.

After accepting the honor and commemorative crystal cube with his name and the College of Science logo etched on it, Viens revealed his latest research to the room full of his colleagues and students. Viens went old-school and used the chalkboard to map out his new work during his presentation, "Long-range Dependence: From Probability Theory, to Quantitative Finance, to Climate Science."

Viens described the work:

"How much 'convincing' evidence can one provide that the atmosphere's temperature is increasing inexorably in response to human-generated greenhouse gases? It could be useful to be convincing about the earth's past climate evolution... On a shorter and more mundane time scale, how can we be sure that politicians are right to take drastic measures when they say they are needed to avoid an impending world-wide economic crash? Having an objective way of measuring anxiety in financial markets could help ... .

"When the complexity of physical, biological, or social phenomena is not adequately described by PDEs or other deterministic systems, the cause may be uncertainty on some of the driving forces. Whether uncertainty itself is due to an inability to observe a determining factor, the inadequacy of quantitative descriptors, or even lacking scientific theory, the problems can benefit from stochastic modeling. Therein, typically, time and its flow of information play a crucial role, and one incorporates uncertainty via random evolutions whose probabilistic laws are well understood. The resulting "stochastic processes" have long been modeled in what is known as the Markovian framework: information from the current state is sufficient to determine the probabilistic laws of future evolutions. This precludes the use of models in which the driving randomness has long-range dependence on the past, or even in space.

"Nevertheless, such dependence is finding an increasing number of advocates in diverse applications ranging from econometrics, to computer engineering, to climate evolution. The mathematics and statistics of these types of models require abandoning classical frameworks such as martingales or Markov processes, but are not beyond reach. Phenomena such as the celebrated central-limit theorem for independent random terms extend partially to long-range dependent systems. To prove theorems in this direction, Gaussian analysis is useful, particularly the so-called Malliavin calculus on Wiener space, a theoretical tool from functional analysis. Empirical techniques deserve close consideration as well, and are sometimes the only recourse in real-life problems. We will present an overview of classical and recent work on the topic of long-range-dependent random models, with applications to memory parameter estimation in mathematical statistics, stochastic volatility tracking in quantitative finance, and paleo-temperature reconstruction in climate science."

**More on Viens**

Viens does not formally hold the equivalent of a US Bachelor's degree. He obtained a Master degree in Pure Mathematics from the University of Paris 7, and a Ph.D. in Mathematics from the University of California at Irvine where he worked on stochastic partial differential equations. Within the community of probabilists, he is best known for his advances in stochastic analysis, a field which studies the chaotic evolution of random models by using infinite-dimensional tools from functional analysis and probability. Viens strives to contribute significantly to applied mathematics, statistics, finance, and other fields. He has recently started pursuing an interest in environmental statistics, and hopes to learn much more. He has published over 50 research articles, does extensive editorial work for top journals and other publishing outlets in his fields, regularly organizes international conferences in stochastic analysis, as well as the yearly High-Frequency Data Analysis in Finance conference. His interest in international outreach has led him to chairing the pure mathematics section for Canada's national grants competition, working for a year as Science Advisor for a regional bureau at the U.S. Department of State in Washington, D.C., and promoting the mathematical sciences and scientific capacity development in sub-Saharan Africa. In his spare time, he enjoys spending time with his family and his avian flock, which includes a cockatiel, a conure, a budgie, a parrotlet, and a dove; this has led to his amateur-level fascination for animal cognition and behavior.

*Prof. Frederi Viens maps out his latest work at the chalkboard.*