First detection of threshold crossing events under intermittent sensing

Abstract

The time of the first occurrence of a threshold crossing event in a stochastic process, known as the first passage time, is of interest in many areas of sciences and engineering. Conventionally, there is an implicit assumption that the notional 'sensor' monitoring the threshold crossing event is always active. In many realistic scenarios, the sensor monitoring the stochastic process works intermittently. Then, the relevant quantity of interest is the $\text{first detection time}$, which denotes the time when the sensor detects the threshold crossing event for the first time. In this work, a birth-death process monitored by a random intermittent sensor is studied, for which the first detection time distribution is obtained. In general, it is shown that the first detection time is related to, and is obtainable from, the first passage time distribution. Our analytical results display an excellent agreement with simulations. Further, this framework is demonstrated in several applications -- the SIS compartmental and logistic models, and birth-death processes with resetting. Finally, we solve the practically relevant problem of inferring the first passage time distribution from the first detection time.

References in corpus (9)

• First Passage Under Restart
• Extreme events on complex networks
• First passage time statistics for two-channel diffusion
• Diffusive search for a stochastically-gated target with resetting
• Preface: New trends in first-passage methods and applications in the life sciences and engineering
• First hitting times to intermittent targets
• A Unified Approach to Gated Reactions on Networks
• First hitting times between a run-and-tumble particle and a stochastically-gated target
• How rare are diffusive rare events?

Cited by in corpus (4)

• Inference from gated first-passage times
• Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime
• Gated reactions in discrete time and space
• Continuous Gated First-Passage Processes