Related papers: Quickest drift change detection in L\'evy-type for…
We study the quickest detection problem of a sudden change in the arrival rate of a Poisson process from a known value to an unknown and unobservable value at an unknown and unobservable disorder time. Our objective is to design an alarm…
Consider the motion of a Brownian particle in two or more dimensions, whose coordinate processes are standard Brownian motions with zero drift initially, and then at some random/unobservable time, one of the coordinate processes gets a…
For the classical continuous-time quickest change-point detection problem it is shown that the randomized Shiryaev-Roberts-Pollak procedure is asymptotically nearly minimax-optimal (in the sense of Pollak 1985) in the class of randomized…
The problem of quickest change detection (QCD) under transient dynamics is studied, where the change from the initial distribution to the final persistent distribution does not happen instantaneously, but after a series of transient phases.…
In this paper, we consider the problem of quickest change point detection and identification over a linear array of $N$ sensors, where the change pattern could first reach any of these sensors, and then propagate to the other sensors. Our…
A novel quickest detection setting is proposed which is a generalization of the well-known Bayesian change-point detection model. Suppose \{(X_i,Y_i)\}_{i\geq 1} is a sequence of pairs of random variables, and that S is a stopping time with…
This paper investigates change point detection in state space models, in which the pre-change distribution $f^{\theta_0}$ is given, while the poster distribution $f^{\theta}$ after change is unknown. The problem is to raise an alarm as soon…
We consider an SDE in R^m of the type dX(t)=a(X(t))dt+dU(t) with a L\'evy process U and study the problem for the distribution of a solution to be regular in various senses. We do not impose any specific conditions on the L\'evy measure of…
In this paper, we study the quickest change detection with mismatched post-change models. A change point is the time instant at which the distribution of a random process changes. The objective of quickest change detection is to minimize…
We study the efficiency of random search processes based on L{\'e}vy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the bias of the searcher…
Last passage times arise in a number of areas of applied probability, including risk theory and degradation models. Such times are obviously not stopping times since they depend on the whole path of the underlying process. We consider the…
Change-point detection methods are proposed for the case of temporary failures, or transient changes, when an unexpected disorder is ultimately followed by a readjustment and return to the initial state. A base distribution of the…
We investigate the problem of covert quickest change detection in a continuous-time setting, where a Brownian motion experiences a drift change at an unknown time. Unlike classical formulations, we consider a covert adversary who adjusts…
We consider one-dimensional discrete-time random walks (RWs) with arbitrary symmetric and continuous jump distributions $f(\eta)$, including the case of L\'evy flights. We study the expected maximum ${\mathbb E}[M_n]$ of bridge RWs, i.e.,…
This paper provides the first description of a weak practical super-martingale phenomenon that can emerge in the test statistic in Shiryaev's Bayesian quickest change detection (QCD) problem. We establish that this super-martingale…
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) spatial coordinate is a standard Brownian motion with a non-zero drift.…
This paper establishes that an exactly optimal rule for Bayesian Quickest Change Detection (QCD) of Markov chains is a threshold test on the no change posterior. We also provide a computationally efficient scalar filter for the no change…
The problem of quickest detection of a change in distribution is considered under the assumption that the pre-change distribution is known, and the post-change distribution is only known to belong to a family of distributions…
The purpose of this paper is to implement a random death process into a persistent random walk model which produces subballistic superdiffusion (L\'{e}vy walk). We develop a Markovian model of cell motility with the extra residence variable…
The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. The pre-change observations are assumed to be stationary with a known distribution, while the post-change…