477 research outputs found
Type II singular perturbation approximation for linear systems with LĂ©vy noise
When solving linear stochastic partial differential equations
numerically, usually a high order spatial discretisation is needed. Model
order reduction (MOR) techniques are often used to reduce the order of
spatially-discretised systems and hence reduce computational complexity. A
particular MOR technique to obtain a reduced order model (ROM) is singular
perturbation approximation (SPA), a method which has been extensively studied
for deterministic systems. As so-called type I SPA it has already been
extended to stochastic equations. We provide an alternative generalisation of
the deterministic setting to linear systems with LĂ©vy noise which is called
type II SPA. It turns out that the ROM from applying type II SPA has better
properties than the one of using type I SPA. In this paper, we provide new
energy interpretations for stochastic reachability Gramians, show the
preservation of mean square stability in the ROM by type II SPA and prove two
different error bounds for type II SPA when applied to LĂ©vy driven systems
Type II singular perturbation approximation for linear systems with LĂ©vy noise
oai:archive.wias-berlin.de:test_mods_00000044When solving linear stochastic partial differential equations numerically, usually a high order spatial discretisation is needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretised systems and hence reduce computational complexity. A particular MOR technique to obtain a reduced order model (ROM) is singular perturbation approximation (SPA), a method which has been extensively studied for deterministic systems. As so-called type I SPA it has already been extended to stochastic equations. We provide an alternative generalisation of the deterministic setting to linear systems with L'evy noise which is called type II SPA. It turns out that the ROM from applying type II SPA has better properties than the one of using type I SPA. In this paper, we provide new energy interpretations for stochastic reachability Gramians, show the preservation of mean square stability in the ROM by type II SPA and prove two different error bounds for type II SPA when applied to L'evy driven system
Balancing Related Model Order Reduction Applied to Linear Controlled Evolution Equations with LĂ©vy Noise
Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Dissertation, 2016von Martin Redmann, M. Sc.Literaturverzeichnis: Blatt 177-18
Energy estimates and model order reduction for stochastic bilinear systems
In this paper, we investigate a large-scale stochastic system with bilinear drift and linear diffusion term. Such high dimensional systems appear for example when discretizing a stochastic partial differential equations in space. We study a particular model order reduction technique called balanced truncation (BT) to reduce the order of spatially-discretized systems and hence reduce computational complexity. We introduce suitable Gramians to the system and prove energy estimates that can be used to identify states which contribute only very little to the system dynamics. When BT is applied the reduced system is obtained by removing these states from the original system. The main contribution of this paper is an L2-error bound for BT for stochastic bilinear systems. This result is new even for deterministic bilinear equations. In order to achieve it, we develop a new technique which is not available in the literature so far
Chance, long tails, and inference: a non-Gaussian, Bayesian theory of vocal learning in songbirds
Traditional theories of sensorimotor learning posit that animals use sensory
error signals to find the optimal motor command in the face of Gaussian sensory
and motor noise. However, most such theories cannot explain common behavioral
observations, for example that smaller sensory errors are more readily
corrected than larger errors and that large abrupt (but not gradually
introduced) errors lead to weak learning. Here we propose a new theory of
sensorimotor learning that explains these observations. The theory posits that
the animal learns an entire probability distribution of motor commands rather
than trying to arrive at a single optimal command, and that learning arises via
Bayesian inference when new sensory information becomes available. We test this
theory using data from a songbird, the Bengalese finch, that is adapting the
pitch (fundamental frequency) of its song following perturbations of auditory
feedback using miniature headphones. We observe the distribution of the sung
pitches to have long, non-Gaussian tails, which, within our theory, explains
the observed dynamics of learning. Further, the theory makes surprising
predictions about the dynamics of the shape of the pitch distribution, which we
confirm experimentally
Constant & time-varying hedge ratio for FBMKLCI stock index futures
This paper examines hedging strategy in stock index futures for Kuala Lumpur Composite Index futures of Malaysia. We employed two different econometric
methods such as-vector error correction model (VECM) and bivariate generalized autoregressive conditional heteroskedasticity (BGARCH) models to estimate
optimal hedge ratio by using daily data of KLCI index and KLCI futures for the period from January 2012 to June 2016 amounting to a total of 1107 observations.
We found that VECM model provides better results with respect to estimating hedge ratio for spot month futures and one-month futures, while BGACH shows
better for distance futures. While VECM estimates time invariant hedge ratio, the BGARCH shows that hedge ratio changes over time. As such, hedger should
rebalance his/her position in futures contract time to time in order to reduce risk exposure
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