4,619 research outputs found
Maturity randomization for stochastic control problems
We study a maturity randomization technique for approximating optimal control
problems. The algorithm is based on a sequence of control problems with random
terminal horizon which converges to the original one. This is a generalization
of the so-called Canadization procedure suggested by Carr [Review of Financial
Studies II (1998) 597--626] for the fast computation of American put option
prices. In addition to the original application of this technique to optimal
stopping problems, we provide an application to another problem in finance,
namely the super-replication problem under stochastic volatility, and we show
that the approximating value functions can be computed explicitly.Comment: Published at http://dx.doi.org/10.1214/105051605000000593 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Lagrangian Time Series Models for Ocean Surface Drifter Trajectories
This paper proposes stochastic models for the analysis of ocean surface
trajectories obtained from freely-drifting satellite-tracked instruments. The
proposed time series models are used to summarise large multivariate datasets
and infer important physical parameters of inertial oscillations and other
ocean processes. Nonstationary time series methods are employed to account for
the spatiotemporal variability of each trajectory. Because the datasets are
large, we construct computationally efficient methods through the use of
frequency-domain modelling and estimation, with the data expressed as
complex-valued time series. We detail how practical issues related to sampling
and model misspecification may be addressed using semi-parametric techniques
for time series, and we demonstrate the effectiveness of our stochastic models
through application to both real-world data and to numerical model output.Comment: 21 pages, 10 figure
Coded Distributed Tracking
We consider the problem of tracking the state of a process that evolves over
time in a distributed setting, with multiple observers each observing parts of
the state, which is a fundamental information processing problem with a wide
range of applications. We propose a cloud-assisted scheme where the tracking is
performed over the cloud. In particular, to provide timely and accurate
updates, and alleviate the straggler problem of cloud computing, we propose a
coded distributed computing approach where coded observations are distributed
over multiple workers. The proposed scheme is based on a coded version of the
Kalman filter that operates on data encoded with an erasure correcting code,
such that the state can be estimated from partial updates computed by a subset
of the workers. We apply the proposed scheme to the problem of tracking
multiple vehicles. We show that replication achieves significantly higher
accuracy than the corresponding uncoded scheme. The use of maximum distance
separable (MDS) codes further improves accuracy for larger update intervals. In
both cases, the proposed scheme approaches the accuracy of an ideal centralized
scheme when the update interval is large enough. Finally, we observe a
trade-off between age-of-information and estimation accuracy for MDS codes.Comment: Accepted for publication at IEEE GLOBECOM 201
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