38,574 research outputs found
Multilevel Particle Filters for L\'evy-driven stochastic differential equations
We develop algorithms for computing expectations of the laws of models
associated to stochastic differential equations (SDEs) driven by pure L\'evy
processes. We consider filtering such processes and well as pricing of path
dependent options. We propose a multilevel particle filter (MLPF) to address
the computational issues involved in solving these continuum problems. We show
via numerical simulations and theoretical results that under suitable
assumptions of the discretization of the underlying driving L\'evy proccess,
our proposed method achieves optimal convergence rates. The cost to obtain MSE
scales like for our method, as compared with
the standard particle filter
Tensor decomposition with generalized lasso penalties
We present an approach for penalized tensor decomposition (PTD) that
estimates smoothly varying latent factors in multi-way data. This generalizes
existing work on sparse tensor decomposition and penalized matrix
decompositions, in a manner parallel to the generalized lasso for regression
and smoothing problems. Our approach presents many nontrivial challenges at the
intersection of modeling and computation, which are studied in detail. An
efficient coordinate-wise optimization algorithm for (PTD) is presented, and
its convergence properties are characterized. The method is applied both to
simulated data and real data on flu hospitalizations in Texas. These results
show that our penalized tensor decomposition can offer major improvements on
existing methods for analyzing multi-way data that exhibit smooth spatial or
temporal features
Momentum Strategies with L1 Filter
In this article, we discuss various implementation of L1 filtering in order
to detect some properties of noisy signals. This filter consists of using a L1
penalty condition in order to obtain the filtered signal composed by a set of
straight trends or steps. This penalty condition, which determines the number
of breaks, is implemented in a constrained least square problem and is
represented by a regularization parameter ? which is estimated by a
cross-validation procedure. Financial time series are usually characterized by
a long-term trend (called the global trend) and some short-term trends (which
are named local trends). A combination of these two time scales can form a
simple model describing the process of a global trend process with some
mean-reverting properties. Explicit applications to momentum strategies are
also discussed in detail with appropriate uses of the trend configurations.Comment: 22 pages, 15 figures. Submitted to The Journal of Investment
Strategies, reference code: JOIS140227T
State estimation of a solar direct steam generation mono-tube cavity receiver using a modified Extended Kalman Filtering scheme
State estimation plays a key role in the development of advanced control strategies for Concentrating Solar Thermal Power (CSP)
systems, by providing an estimate of process variables that are otherwise infeasible to measure. The present study proposes a state estimation
scheme for a once-through direct steam generation plant, the SG4 steam generation system at the Australian National University.
The state estimation scheme is a modified Extended Kalman Filter that computes an estimate of the internal variables of the mono-tube
cavity receiver in the SG4 system, from a dynamic non-linear model of the receiver. The proposed scheme augments the capabilities of a
Continuous-Direct Extended Kalman Filter to deal with the switched nature of the receiver, in order to produce estimates during system
start-up, cloud transients and operation of the plant. The estimation process runs at regular sample intervals and happens in two stages, a
prediction and a correction stage. The prediction stage uses the receiver model to calculate the evolution of the system and the correction
stage modifies the predicted estimate from measurements of the SG4 system. The resulting estimate is a set of internal variables describing
the current state of the receiver, termed the state vector. This paper presents a description of the modified Extended Kalman Filter
and an evaluation of the scheme using computer simulations and experimental runs in the SG4 system. Simulations and experimental
results in this paper show that the filtering scheme improves a receiver state vector estimation purely based on the receiver model
and provides estimates of a quality sufficient for closed loop control.This work has been supported by the Australian
Renewable Energy Agency (ARENA)
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