weak convergence

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 17, 2018 - 10:30am - 11:00am
Guodong Pang (The Pennsylvania State University)
The method of chaining is often used to obtain probability and moment bounds for stochastic processes. We explore the application of the chaining bounds in non-Markovian many-server queues. In these models, we study two-parameter stochastic processes that can be used to describe the service dynamics, in particular, X(t,y) representing the number of jobs in the system at time t that have received an amount of service less than or equal to y (or that have a residual amount of service strictly greater than y).
Monday, May 7, 2018 - 3:00pm - 3:30pm
Chao Zhu (University of Wisconsin, Milwaukee)
This work considers an optimal inventory control problem using a long-term average criterion. In absence of ordering, the inventory process is modeled by a one-dimensional diffusion on some interval of $(-\infty, \infty)$ with general drift and diffusion coefficients and boundary points that are consistent with the notion that demands tend to reduce the inventory level. Orders instantaneously increase the inventory level and incur both positive fixed and level dependent costs. In addition, state-dependent holding/backorder costs are incurred continuously.
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