RESEARCH

My primary research interests lie in probability theory, analysis of stochastic processes, and the underlying mathematics: in short, the study of randomness. My past work focuses on the reliability of stochastic networks, renewal theory, random walks, stochastic game theory, stochastic measure theory, and particularly the application of discrete and continuous operational calculus to stochastic processes. I continue research in these areas, but my new projects are focused on random geometry, probability flux, intrusion detection, deep learning, and probabilistic potential theory in parabolic PDEs.

Presentations
  • On the Evolution of Minimal-Volume, Sufficient-Probability Sets for Stochastic Paths.14th International Conference in Monte Carlo & Quasi-Monte Carlo Methods in Scientific Computing, University of Oxford, United Kingdom. 10-14 Aug 2020 [Slides]

  • Fluctuation Analysis in Parallel Queues with Hysteretic Control. AMS Fall Southeastern Sectional Meeting, University of Florida, Gainesville, Florida. 2-3 Nov 2019 [Slides]

  • On Exits of Oscillating Random Walks Under Delayed Observation. AMS/MAA Joint Mathematical Meetings, San Diego, California, 10-13 Jan 2018 [Slides]

  • Time Sensitive Analysis of d-dim Independent and Stationary Increment Processes. AMS Fall Southeastern Sectional Meeting,  University of Central Florida, Orlando, Florida. 23-24 Sept 2017. [Slides]

  • Random Walks on Random Lattices and Their Applications. FIT MTH/ORP Graduate Student Seminar. 21 Apr 2015 [Slides]

  • Time Sensitive Analysis of Multivariate Marked Random Walks. SIAM Conference on Computational Science and Engineering. Salt Lake City, UT. 14-18 Mar 2015 [Slides]

  • Time Sensitive Analysis of ISI Processes. FIT Mathematical Sciences Symposium. 8 Jan 2015 [Slides]

  • Random Walks on Random Lattices: An Operational Calculus Approach. FIT MTH/ORP Graduate Student Seminar. 30 Sept 2014 [Slides]

  • Stochastic Analysis of Strategic Networks. 38th Annual SIAM Southeastern Atlantic Section Conference. Florida Institute of Technology, Melbourne, FL. 29-30 Mar, 2014 [Slides]

Academic Papers
(expand for details and PDFs as publishing agreements allow)
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