Change Detection of Markov Kernels with Unknown Pre and Post Change Kernel
This work addresses change detection in stochastic processes for applications like monitoring and control, but it appears incremental as it builds on existing methods by handling unknown post-change kernels.
The paper tackles the problem of detecting changes in Markov kernels when the post-change kernel is unknown, deriving bounds on mean delay and false alarm time under uniform ergodicity assumptions, with numerical simulations demonstrating effectiveness.
In this paper, we develop a new change detection algorithm for detecting a change in the Markov kernel over a metric space in which the post-change kernel is unknown. Under the assumption that the pre- and post-change Markov kernel is uniformly ergodic, we derive an upper bound on the mean delay and a lower bound on the mean time between false alarms. A numerical simulation is provided to demonstrate the effectiveness of our method.