Speaker: Devika Khurana (University of Oslo)
Title: First-passage times of stochastic dynamical systems to time-dependent thresholds
Abstract: First-passage time (FPT) describes the time at which a stochastic process reaches a specified threshold for the first time. In many applications, however, the relevant threshold evolves over time, motivating the study of first-passage problems with time-dependent boundaries.
In this talk, I will consider first-passage time problems for two classes of stochastic processes: stochastic differential equations (SDEs) and piecewise-diffusion Markov processes (PDifMPs), with a particular focus on exact simulation. For SDEs with a constant threshold, an exact simulation approach can be constructed using the known first-passage time distribution of Brownian motion as a proposal distribution. A candidate first-passage time is generated from the corresponding Brownian motion and accepted as the first-passage time of the target process according to an acceptance probability derived via Girsanov’s theorem.
We extend this approach to SDEs with time-dependent thresholds and then use this extension to develop an exact simulation method for PDifMPs with time-dependent thresholds. The resulting framework enables direct simulation of first-passage times without requiring the simulation of entire sample paths over a prescribed time interval and without introducing time-discretisation error.
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