Research & Publications

I am a probabilist working at the intersection of stochastic processes, random dynamical systems, and mathematical ecology.

Recently, I have used tools from stochastic differential equations, random dynamical systems, ordinary differential equations, partial differential equations, and optimal control in order to explore the dynamics of populations that are affected by random environmental fluctuations.

I am also interested in the long-term behaviour of Markov processes (stationary distributions, quasistationary distributions, ergodic properties).

Stochastic population dynamics

  1. Harvesting and seeding of stochastic populations: analysis and numerical approximation, with Ky Tran, preprint, 2019.
  2. A general theory of coexistence and extinction for stochastic ecological communities, with Peter Chesson and Dang H. Nguyen, preprint, 2019.
  3. A classification of the dynamics of three dimensional stochastic Lotka-Volterra systems, with Dang H. Nguyen and Sebastian J. Schreiber, preprint, 2019.
  4. Coevolution of Patch Selection in Stochastic Environments, with Dang H. Nguyen and Sebastian J. Schreiber, preprint, 2019.
  5. Optimal sustainable harvesting of populations in random environments, with Luis H. R. Alvarez E., Stochastic Processes and their Applications  (to appear), 2019, arXiv: 1807.024640
  6. Harvesting of interacting stochastic populations, with Ky Tran, Tien Phan, and George Yin, Journal of Mathematical Biology, Vol. 79, Issue 2, 533-570, 2019, or arXiv: 1810.05609.
  7. The competitive exclusion principle in stochastic environments, with Dang H. Nguyen, Journal of Mathematical Biology (under revision), 2018, arXiv: 1810.00954.
  8. Asymptotic harvesting of populations in fluctuating environments, with Dang H. Nguyen, Sergiu C. Ungureanu and Tak Kwong Wong, Journal of Mathematical Biology,Vol. 78, Issue 1–2, 293–329, 2019, or arXiv: 1710.01221.
  9. On a predator-prey system with random switching that never converges to its equilibrium, with Edouard Strickler, SIAM Journal on Mathematical Analysis (to appear), 2019, arXiv: 1710.01220.
  10. Persistence in stochastic Lotka-Volterra food chains with intraspecific competition, with Dang H. Nguyen, Bulletin of Mathematical Biology, Volume 80, Issue 10, 2527–2560, 2018, or arXiv: 1704.07501.
  11. Coexistence and extinction for stochastic Kolmogorov systems, with Dang H. NguyenAnnals of Applied Probability, Vol. 28, No. 3, 1893-1942, 2018, or arXiv: 1704.06984.
  12. Stochastic Lotka-Volterra food chains, with Dang H. Nguyen, Journal of Mathematical Biology, Volume 77, Issue 1, 135-163, 2018, or arXiv: 1703.04809.
  13. Stochastic population growth in spatially heterogeneous environments: The density-dependent case, with Dang H. Nguyen and George Yin, Journal of Mathematical Biology, Volume 76, Issue 3, 697–754, 2018, or arXiv: 1605.02027.
  14. Protected polymorphisms and evolutionary stability of patch-selection strategies in stochastic environments, with Steven N. Evans and Sebastian J. SchreiberJournal of Mathematical Biology, 71, Issue 2, 325-359, 2015, or arXiv: 1404.6759.

Stochastic processes

  1. Dynamical systems with fast switching and slow diffusion: hyperbolic equilibria and stable limit cycles, with Dang H. Nguyen, Nguyen H. Du and George Yin, submitted, 2019,  arXiv: 1902.01755.
  2. The Inverse First Passage Time Problem for killed Brownian motion, with Boris Ettinger and Tak Kwong Wong Annals of Applied Probability (under revision), 2018,  arXiv: 1807.05438.
  3. Markov processes conditioned on their location at large exponential times, with Steven N. Evans, Stochastic Processes and their Applications, Volume 129, Issue 5, 2019, 1622-1658, or arXiv: 1607.03545.
  4. Quasistationary distributions for one-dimensional diffusions with two singular boundary points, with Martin Kolb, Stochastic Processes and their Applications, Volume 129, Issue 5, 2019, 1659-1696, or arXiv: 1409.2387.
  5. The free path in a high velocity random flight process associated to a Lorentz gas in an external field, with Douglas Rizzolo and Eric S. Wayman, Transactions of the American Mathematical Society, Series B 3 (2016), 27-62 , or arXiv: 1503.02343.
  6. Transient one-dimensional diffusions conditioned to converge to a different limit point, Statistics and Probability Letters, 110, 62-73, 2016, or arXiv: 1510.00273.
  7. When do skew-products exist?, with Steven N. Evans and Eric S. Wayman, Electronic Communications in Probability, 20, no. 54, 1-14, 2015, or arXiv: 1408.6507.
  8. Killed Brownian motion with a prescribed lifetime distribution and models of default, with Boris Ettinger and Steven N. Evans, Annals of Applied Probability, 24, 1-33, 2014, or arXiv: 1111.2976.
  9. Non-existence of Markovian time dynamics for graphical models of correlated default, with Steven N. Evans, Queueing Systems, December 2011, Volume 69, Issue 3-4, 293-312, or arXiv: 1008.2226.
  10. A stochastic Lotka-Volterra system with killing, with Martin Kolb, preprint, 2014, arXiv: 1409.2387.

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