Random ordinary differential equations (RODEs) are ordinary differential equations that include a stochastic process in their vector field. They seem to have had a shadow existence to Ito stochastic differential equations, but have been around for as long as if not longer and have many important applications. In the engineering and physics literature, a simpler kind of RODE is investigated with the vector field being chosen randomly rather than depending on a stochastic process that give rises to stochastic ordinary differential equations (SODEs). Unlike SODEs, RODEs can be analyzed pathwise with deterministic calculus but require further treatment beyond that of classical ODE theory. The sample paths of RODEs may be just Holder continuous and not even differentiable, and thus classical Taylor expansions do not apply. In this lecture we will introduce the special Taylor expansions for RODEs and use them to derive higher order numerical schemes. Convergence analysis will also be provided.
20/07/2020
The webinar can be reached at this Goggle Meet link:
meet.google.com/fyg-xgcy-uyh
at 4:00pm (Italian time)
Xiaoying Han received her B.E. in computer science from the special class for the gifted young of university of science and technology of China, and Ph.D. in applied mathematics from State University of New York at Buffalo. She joined the department of mathematics and statistics at Auburn University in 2007 and is currently a professor of mathematics at Auburn University. Xiaoying Han’s research specialty lies in analysis and simulation of nonautonomous/random differential equations and infinite dimensional dynamical systems with applications in the applied sciences. She was named the 2018-2020 Margurite Scharnagle Endowed Professor of Auburn University, and awarded the 2020-2021 U.S. Fulbright scholar.