Spatiotemporal instabilities in neural fields and the effects of additive noise

Contradictious results published by different authors about the dynamics of systems with random parameters have been examined. Statistical analysis of the simple 1st order system proves that the random parameter can cause a systematic difference in the dynamic behavior that cannot be (in general) described by the usual constant-parameter model with the additive noise at the output.

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Stochastic sensitivity of bull and bear states

Journal of Economic Interaction and Coordination ◽

10.1007/s11403-020-00313-2 ◽

2021 ◽

Author(s):

Jochen Jungeilges ◽

Elena Maklakova ◽

Tatyana Perevalova

Keyword(s):

Additive Noise ◽

Asset Price ◽

Market Model ◽

Asset Market ◽

Stochastic Version ◽

Market Participants ◽

Price Process ◽

Stochastic Sensitivity ◽

Stable Equilibria ◽

Parametric Noise

AbstractWe study the price dynamics generated by a stochastic version of a Day–Huang type asset market model with heterogenous, interacting market participants. To facilitate the analysis, we introduce a methodology that allows us to assess the consequences of changes in uncertainty on the dynamics of an asset price process close to stable equilibria. In particular, we focus on noise-induced transitions between bull and bear states of the market under additive as well as parametric noise. Our results are obtained by combining the stochastic sensitivity function (SSF) approach, a mixture of analytical and numerical techniques, due to Mil’shtein and Ryashko (1995) with concepts and techniques from the study of non-smooth 1D maps. We find that the stochastic sensitivity of the respective bull and bear equilibria in the presence of additive noise is higher than under parametric noise. Thus, recurrent transitions are likely to be observed already for relatively low intensities of additive noise.

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Additive noise effect in digital phase detection

Applied Optics ◽

10.1364/ao.36.000271 ◽

1997 ◽

Vol 36 (1) ◽

pp. 271 ◽

Cited By ~ 83

Author(s):

Yves Surrel

Keyword(s):

Additive Noise ◽

Phase Detection ◽

Noise Effect ◽

Digital Phase ◽

Digital Phase Detection

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Scalable Gaussian Process Classification With Additive Noise for Non-Gaussian Likelihoods

IEEE Transactions on Cybernetics ◽

10.1109/tcyb.2020.3043355 ◽

2021 ◽

pp. 1-13

Author(s):

Haitao Liu ◽

Yew-Soon Ong ◽

Ziwei Yu ◽

Jianfei Cai ◽

Xiaobo Shen

Keyword(s):

Gaussian Process ◽

Additive Noise ◽

Non Gaussian ◽

Process Classification

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Inverse problems for stochastic parabolic equations with additive noise

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip-2017-0003 ◽

2020 ◽

Vol 29 (1) ◽

pp. 93-108

Author(s):

Ganghua Yuan

Keyword(s):

Inverse Problems ◽

Parabolic Equations ◽

Additive Noise ◽

Stability Result ◽

Main Tool ◽

Conditional Stability ◽

Final Time ◽

History Of ◽

Global Carleman Estimate ◽

Stochastic Parabolic Equation

Abstract In this paper, we study two inverse problems for stochastic parabolic equations with additive noise. One is to determinate the history of a stochastic heat process and the random heat source simultaneously by the observation at the final time 𝑇. For this inverse problem, we obtain a conditional stability result. The other one is an inverse source problem to determine two kinds of sources simultaneously by the observation at the final time and on the lateral boundary. The main tool for solving the inverse problems is a new global Carleman estimate for the stochastic parabolic equation.

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Early Detection of Defects through the Identification of Distortion Characteristics in Ultrasonic Responses

Mathematics ◽

10.3390/math9080850 ◽

2021 ◽

Vol 9 (8) ◽

pp. 850

Author(s):

Pietro Burrascano ◽

Matteo Ciuffetti

Keyword(s):

Early Detection ◽

Additive Noise ◽

Linear Models ◽

High Stress ◽

Damage Index ◽

Hammerstein Model ◽

Linear Behavior ◽

Non Linear ◽

Ultrasonic Techniques ◽

Detection Of Defects

Ultrasonic techniques are widely used for the detection of defects in solid structures. They are mainly based on estimating the impulse response of the system and most often refer to linear models. High-stress conditions of the structures may reveal non-linear aspects of their behavior caused by even small defects due to ageing or previous severe loading: consequently, models suitable to identify the existence of a non-linear input-output characteristic of the system allow to improve the sensitivity of the detection procedure, making it possible to observe the onset of fatigue-induced cracks and/or defects by highlighting the early stages of their formation. This paper starts from an analysis of the characteristics of a damage index that has proved effective for the early detection of defects based on their non-linear behavior: it is based on the Hammerstein model of the non-linear physical system. The availability of this mathematical model makes it possible to derive from it a number of different global parameters, all of which are suitable for highlighting the onset of defects in the structure under examination, but whose characteristics can be very different from each other. In this work, an original damage index based on the same Hammerstein model is proposed. We report the results of several experiments showing that our proposed damage index has a much higher sensitivity even for small defects. Moreover, extensive tests conducted in the presence of different levels of additive noise show that the new proposed estimator adds to this sensitivity feature a better estimation stability in the presence of additive noise.

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