Research Overview

My research focuses on stability issues for stochastic differential equations. In particular, I study a class of deterministic systems which exhibit unstable behavior, but which are stabilized by a small white noise perturbation. This is quite a surprising and intriguing phenomenon because one’s first intuition is often that noise will destabilize, rather than stabilize, a system. I have developed a generalized algorithm for the construction of a global Lyapunov function which can be used to prove the stability of a wide class of stochastic differential equations.  More generally, I am interested in analyzing systems from biology or other applications where noise creates any cohesive behavior which qualitatively differs from that of the unperturbed systems. I am also very interested in mentoring undergraduate research.

Undergraduate Research Projects Mentored

  • Caleb VanArragon, Analysis of the Hot Hand and Cold Hand in Collegiate Golf Tournaments, 2021
  • Ashley Darnell, Community Risk Assessment for the Valparaiso Fire Department, 2021
  • Julia Garner, Victor Hughes, Daniel Meskill, Stabilization of Hamiltonian Systems with Multiplicative Noise, 2019
  • Anthony Coniglio, Sarah Sparks, Daniel Weithers, Noise-Induced Stabilization of Perturbed Hamiltonian Systems, 2017
  • Tony Allen, Emily Gebhardt, Adam Kluball, Minimal Noise-Induced Stabilization of One-Dimensional Diffusions, 2015
  • Kaylyn Banaszak, Anna Kaniewski, Probabilistic Analysis of Polyovulation Frequencies, 2015
  • Hannah Dorman, Nicolle Kinzel, Kathryn Merkling, Statistical Analysis of the Effect of AP Calculus on Performance in College Calculus Courses, 2013
  • Ruyue Yuan, Probabilistic Modeling of the Economic Impact of Earthquakes, 2013
  • Stephanie Volz, Forecasting the 2012 Presidential Election, 2012
  • Jordann Kokoski, Modeling Neuron Firing by a Double-Well Potential, 2011

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