Related papers: Bayesian quickest detection problems for some diff…
We consider a small extent sensor network for event detection, in which nodes take samples periodically and then contend over a {\em random access network} to transmit their measurement packets to the fusion center. We consider two…
Let $Z=(Z_t)_{t\ge0}$ be a regular diffusion process started at $0$, let $\ell$ be an independent random variable with a strictly increasing and continuous distribution function $F$, and let $\tau_{\ell}=\inf\{t\ge0\vert Z_t=\ell\}$ be the…
We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and negative axis, yet discontinuous at zero. This threshold…
We obtain the first probabilistic proof of continuous differentiability of time-dependent optimal boundaries in optimal stopping problems. The underlying stochastic dynamics is a one-dimensional, time-inhomogeneous diffusion. The gain…
This paper considers the constrained sampling multi-stream quickest change detection problem, also known as the bandit quickest change detection problem. One stream contains a change-point that shifts its mean by an unknown amount. The goal…
We show that the optimal decision policy for several types of Bayesian sequential detection problems has a threshold switching curve structure on the space of posterior distributions. This is established by using lattice programming and…
Considering a real-valued diffusion, a real-valued reward function and a positive discount rate, we provide an algorithm to solve the optimal stopping problem consisting in finding the optimal expected discounted reward and the optimal…
We study a problem when a solution to optimal stopping problem for one-dimensional diffusion will generate by threshold strategy. Namely, we give necessary and sufficient conditions under which an optimal stopping time can be specified as…
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…
The classical problem of quickest change detection is studied with an additional constraint on the cost of observations used in the detection process. The change point is modeled as an unknown constant, and minimax formulations are proposed…
Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…
The problem of disorder seeks to determine a stopping time which is as close as possible to the unknown time of ``disorder'' when the observed process changes its probability characteristics. We give a partial answer to this question for…
Algorithms are developed for the quickest detection of a change in statistically periodic processes. These are processes in which the statistical properties are nonstationary but repeat after a fixed time interval. It is assumed that the…
We consider the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution. This problem is investigated in a sequential setup under mild assumptions on the underlying random process. The…
A novel unified Bayesian framework for network detection is developed, under which a detection algorithm is derived based on random walks on graphs. The algorithm detects threat networks using partial observations of their activity, and is…
We consider the problem of detecting an abrupt change in the distribution of a sequentially observed stochastic process. We establish the optimality of the CUSUM test with respect to a modified version of Lorden's criterion for arbitrary…
The problem of detecting a single anomalous process among multiple independent processes is considered. Under a constraint on the number of processes that can be probed simultaneously, the decision maker should decide which processes to…
A solution to the optimal problem for determining vector fields which maximize (resp. minimize) the transition probabilities from one location to another for a class of reflecting diffusion processes is obtained in the present paper. The…
We consider the quickest change detection problem where both the parameters of pre- and post- change distributions are unknown, which prevents the use of classical simple hypothesis testing. Without additional assumptions, optimal solutions…
In this paper, we solve explicitly the optimal stopping problem with random discounting and an additive functional as cost of observations for a regular linear diffusion. We also extend the results to the class of one-sided regular Feller…