Martingales on Jump Processes. II: Applications

Boel, René; Varaiya, Pravin; Wong, Eugene

doi:10.1137/0313064

Cited by 74 publications

(30 citation statements)

References 21 publications

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“…Aspects of the problem of deciding between two hypotheses regarding point processes, one corresponding to a message "all clear" and the other to "alarm," are studied in [3], [7]- [11]. The common idea in all these works is finding the right likelihood ratio, computing it based on the sensor data, and comparing this ratio with a carefully selected threshold.…”

Section: Introductionmentioning

confidence: 99%

Error probabilities and threshold selection in networked nuclear detection

Pahlajani

Sun

Poulakakis

et al. 2013

52nd IEEE Conference on Decision and Control

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Abstract-We consider the problem of computing analytical bounds on error probabilities in the setting of networked nuclear detection based on a likelihood ratio test. The detection scenario involves a mobile source of known trajectory passing within the sensing range of a spatially distributed sensor array, which has to decide on its nature (benign or radioactive) within a fixed time interval. Exploiting the particular modeling structure of remote nuclear measurement, and the form that the likelihood ratio takes in this setting, the paper presents analytical Chernoff bounds for the error probabilities, which in turn allow the selection of threshold constants for the likelihood ratio test in a computationally efficient manner compared to Monte Carlo simulations.

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Section: Introductionmentioning

confidence: 99%

Error probabilities and threshold selection in networked nuclear detection

Pahlajani

Sun

Poulakakis

et al. 2013

52nd IEEE Conference on Decision and Control

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“…In [77] an existence theorem along the lines of (4.20) is obtained; however this only holds under very restrictive assumptions, related to the absolute continuity of the measures. In the Brownian case all the measures P are mutualtvy absolutely continuous under very natural conditions, u and this is crucial in the proof of the existence result, as is seen in (4.18), (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19).…”

Section: Jump Processesmentioning

confidence: 99%

“…In the literature [12], [22], [77] various forms of Hamiltonian appear, depending on the nature of the cost function and the function ~. In [77] an existence theorem along the lines of (4.20) is obtained; however this only holds under very restrictive assumptions, related to the absolute continuity of the measures.…”

Section: Jump Processesmentioning

confidence: 99%

“…is an Ft-martingale for a suitable class of predictable integrands g, and the martingaZe representation theorem [12], [171], [47] states that all Ft-martingales are of this form for some g.…”

Section: Jump Processesmentioning

confidence: 99%

“…We will mention more specific results for special cases below; see also references [2], [3], [12], [13], [30], [36], · [43], [56], [60], 1277]. [ 64,III 102].…”

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confidence: 99%

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Martingale methods in stochastic control

Davis

Lecture Notes in Control and Information Sciences

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The martingale treatment of stochastic control problems is based on the idea that the correct formulation of Bellman's "principle of optiraality" for stochastic minimization problems is in terms of a submartingale inequality: the "value function" of dynamic programming is always a submartingale and is a martingale under a particular control strategy if and only if that strategy is optimal. Local conditions for optimality in the form of a minimum principle can be obtained by applying Meyer's submartingale decomposition along with martingale representation theorems; conditions for existence of an optimal strategy can also be stated. This paper gives an introduction to these methods and a survey of the results that have been obtained so far, as well as an indication of some shortcomings in the theory and open problems. By way of introduction we treat systems of controlled stochastic differential equations, the case for which the most definitive results have been obtained so far. We then outline a general semimartingale formulation of controlled processes, state some optimality conditions and indicate their application to other specific cases such as that of controlled jump processes.The martingale approach to some related problems -optimal stopping, impulse control and stochastic differential games -will also be outlined.

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2005

Counting Processes and Survival Analysis

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Martingales on Jump Processes. II: Applications

Cited by 74 publications

References 21 publications

Error probabilities and threshold selection in networked nuclear detection

Error probabilities and threshold selection in networked nuclear detection

Martingale methods in stochastic control

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