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We consider the stochastic wave equation on the real line driven by space time white noise and with irregular initial data. We give bounds on higher moments and, for the hyperbolic Anderson model, explicit formulas for second moments. These bounds imply we ...
The characteristic functional is the infinite-dimensional generalization of the Fourier transform for measures on function spaces. It characterizes the statistical law of the associated stochastic process in the same way as a characteristic function specif ...
We adopt an innovation-driven framework and investigate the sparse/compressible distributions obtained by linearly measuring or expanding continuous-domain stochastic models. Starting from the first principles, we show that all such distributions are neces ...
We consider settings where a collective intelligence is formed by aggregating information contributed from many independent agents, such as product reviews, community sensing or opinion polls. To encourage participation and avoid selection bias, agents sho ...
Distributionally robust optimization is a paradigm for decision-making under uncertainty where the uncertain problem data is governed by a probability distribution that is itself subject to uncertainty. The distribution is then assumed to belong to an ambi ...
Increasingly detailed consumer information makes sophisticated price discrimination possible. At fine levels of aggregation, demand may not obey standard regularity conditions. We propose a new randomized sales mechanism for such environments. Bidders can ...
This paper presents a novel probabilistic framework for localizing multiple speakers with a microphone array. In this framework, the generalized cross correlation function (GCC) of each microphone pair is interpreted as a probability distribution of the ti ...
We study the steady-state probability distribution of diffusion and consensus strategies that employ constant step-sizes to enable continuous adaptation and learning. We show that, in the small step-size regime, the estimation error at each agent approache ...
Automatic vehicle identification (AVI) systems are increasingly used for the collection of traffic data in urban and freeway networks. Several methods have been proposed for the estimation of travel times from AVI data, mainly for freeways. The problem of ...
We consider the capacity planning of telecommunications networks with linear investment costs and uncertain future traffic demands. Transmission capacities must be large enough to meet, with a high quality of service (QoS), the range of possible demands, a ...
