The real-time detection of changes in a noisily observed signal is an important problem in
applied science and engineering. The study of parametric optimal detection theory began in …

We study the Bayesian problems of detecting a change in the drift rate of an observable
diffusion process with linear and exponential penalty costs for a detection delay. The optimal …

In the present monograph, which most directly relates to the probabilistic-statistical fields
known as “decision theory” and “statistical sequential analysis,” the main focus is on those …

We introduce a mean field game for a family of filtering problems related to the classic
sequential testing of the drift of a Brownian motion. To the best of our knowledge this work …

Consider the motion of a Brownian particle in three dimensions, whose two spatial
coordinates are standard Brownian motions with zero drift, and the remaining (unknown) …

Consider the motion of a Brownian particle that takes place either in a two-dimensional
plane or in three-dimensional space. Given that only the distance of the particle to the origin …

We study a two-dimensional discounted optimal stopping problem related to the pricing of
perpetual commodity equities in a model of financial markets in which the behaviour of the …

This paper studies a two-player zero-sum Dynkin game arising from pricing an option on an
asset whose rate of return is unknown to both players. Using filtering techniques, we first …

We study the perpetual American call option pricing problem in a model of a financial market
in which the firm issuing a traded asset can regulate the dividend rate by switching it …

We consider a one-dimensional Brownian motion, having a random and unobservable drift
which can take one of three known values. Assuming that we monitor the position of the …