The MSRC regularly hosts Colloquium talks and research conferences. In this academic year, they typically take place on Monday between 4-5 pm in MAPTC 0G/018.

Upcoming:

Date: 2 December 2024

Speaker: Cónall Kelly (University College Cork)
Title: "Nonlinear stochastic systems subject to shocks"
Abstract: "Stochastic differential equations (SDEs) are used to model the evolution of real-world phenomena subject to random noise and uncertainty. Consider, for example, asset prices or stochastic interest rates in finance, models of ecological systems with complex interactions between species, or models of chemical reactions in biological cells. The random noise may act as a diffusion, reflecting market volatility, or as a jump process when an ecosystem is influenced by a random external event. For most nonlinear SDEs, there is no closed-form solution, and typically numerical methods are used by modelers. However, standard schemes based on solving to a final time using a uniform step size are not applicable for highly nonlinear systems, and the methods that do exist are often inefficient.

In this talk, we discuss the use of adaptive mesh construction strategies for SDEs that are subject to impulsive shocks at random intervals. These shocks can either take the form of direct perturbation by a jump process or, in another setting, as systemic shifts modeled in SDE coefficients according to the evolution of a Markov chain. We will motivate and characterize these strategies and provide a strong convergence analysis for numerical methods implemented on the random meshes they generate. Implementation will be illustrated via a model of telomere shortening in jackdaws. This is joint work with Gabriel Lord (Radboud University), Kate O’Donovan (UCC), and Fandi Sun (Heriot-Watt University)."