Monday, June 4, 2018 - 3:00pm - 3:30pm
Dang Hai Nguyen (Wayne State University)
We consider asymptotic behaviors of some interacting populations in a fluctuating environment, which are described by Kolmogorov systems with white noise (stochastic differential equations) By analyzing the dynamics of the solution near the boundary and by determining Lyapunov exponents with respect to invariant probability measures on the boundary, we obtain conditions for both persistence and extinction of species. The conditions are sharp in the sense that only critical cases remain unsolved.
Monday, June 4, 2018 - 2:30pm - 3:00pm
Alexandru Hening (Tufts University)
We consider the harvesting of a population in a stochastic environment whose dynamics in the absence of harvesting is described by a one dimensional diffusion. Using ergodic optimal control, we find the optimal harvesting strategy which maximizes the asymptotic yield of harvested individuals.
Thursday, May 17, 2018 - 10:00am - 10:30am
Fuke Wu (Huazhong University of Science and Technology)
Dupire recently developed a functional Ito formula, which has changed the landscape of the study of stochastic functional equations and encouraged a reconsideration of many problems and applications. Delays are ubiquitous, pervasive, and entrenched in everyday life. Based on the new development, this work examines functional diffusions with two-time scales in which the slow-varying process includes path-dependent functionals and the fast-varying process is a rapidly-changing diffusion.
Thursday, May 10, 2018 - 3:00pm - 3:30pm
Dang Hai Nguyen (Wayne State University)
This talk deals with optimal harvesting strategies for the predator in a predator-prey system. The objective function is of long-run average per unit time type in the path-wise sense.
The ecological system is subject to environmental noise modeled as stochastic differential equations driven by a Brownian motion. The main result is to prove the existence and uniqueness of solutions to the .Hamilton–Jacobi–Bellman equation associated with the controlled stochastic system.
The existence of optimal Markov strategies is also derived.

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