scholarly journals The maximum distribution of a Gaussian stochastic process indexed by a local field

1989 ◽  
Vol 46 (1) ◽  
pp. 69-87 ◽  
Author(s):  
Steven N. Evans
Keyword(s):  
Stochastic Process ◽  
Vector Space ◽  
Compact Subset ◽  
Local Field ◽  
Asymptotic Expression ◽  
Independent Interest ◽  
Gaussian Stochastic Process ◽  
High Level

AbstractWe consider continuous Gaussian stochastic process indexed by a compact subset of a vector space over a local field. Under suitable conditions we obtain an asymptotic expression for the probability that such a process will exceed a high level. An important component in the proof of these results is a theorem of independent interest concerning the amount of ‘time’ which the process spends at high levels.

scholarly journals Robust Gaussian stochastic process emulation

2018 ◽  
Vol 46 (6A) ◽  
pp. 3038-3066 ◽  
Author(s):  
Mengyang Gu ◽  
Xiaojing Wang ◽  
James O. Berger
Keyword(s):  
Stochastic Process ◽  
Gaussian Stochastic Process

On the modeling of linear system input stochastic processes with given accuracy and reliability

2018 ◽  
Vol 24 (2) ◽  
pp. 129-137
Author(s):  
Iryna Rozora ◽  
Mariia Lyzhechko
Keyword(s):  
Banach Space ◽  
Stochastic Process ◽  
Linear System ◽  
Stochastic Processes ◽  
Impulse Response Function ◽  
Output Process ◽  
Gaussian Stochastic Process ◽  
System Input ◽  
Time Invariant ◽  
Gaussian Stochastic Processes

AbstractThe paper is devoted to the model construction for input stochastic processes of a time-invariant linear system with a real-valued square-integrable impulse response function. The processes are considered as Gaussian stochastic processes with discrete spectrum. The response on the system is supposed to be an output process. We obtain the conditions under which the constructed model approximates a Gaussian stochastic process with given accuracy and reliability in the Banach space{C([0,1])}, taking into account the response of the system. For this purpose, the methods and properties of square-Gaussian processes are used.

An Upper Bound on the Failure Probability for Linear Structures

1973 ◽  
Vol 40 (1) ◽  
pp. 181-185 ◽  
Author(s):  
L. H. Koopmans ◽  
C. Qualls ◽  
J. T. P. Yao
Keyword(s):  
Stochastic Process ◽  
Failure Probability ◽  
Upper Bound ◽  
Impulse Response Function ◽  
Linear Structures ◽  
Stochastic Response ◽  
Gaussian Stochastic Process ◽  
Exponential Bound ◽  
Mean And Variance ◽  
The Mean

This paper establishes a new upper bound on the failure probability of linear structures excited by an earthquake. From Drenick’s inequality max|y(t)| ≤ MN, where N2 = ∫h2, M2, = ∫x2, x(t) is a nonstationary Gaussian stochastic process representing the excitation of the earthquake, and y(t) is the stochastic response of the structure with impulse response function h(τ), we obtain an exponential bound computable in terms of the mean and variance of the energy M2. A numerical example is given.

scholarly journals NetPyNE Implementation and Scaling of the Potjans-Diesmann Cortical Microcircuit Model

2021 ◽  
pp. 1-40
Author(s):  
Cecilia Romaro ◽  
Fernando Araujo Najman ◽  
William W. Lytton ◽  
Antonio C. Roque ◽  
Salvador Dura-Bernal
Keyword(s):  
Local Field ◽  
Large Scale ◽  
Field Potential ◽  
Network Size ◽  
Model Parameters ◽  
Neuron Models ◽  
Cortical Microcircuit ◽  
Optimizing Model ◽  
New Research ◽  
High Level

Abstract The Potjans-Diesmann cortical microcircuit model is a widely used model originally implemented in NEST. Here, we reimplemented the model using NetPyNE, a high-level Python interface to the NEURON simulator, and reproduced the findings of the original publication. We also implemented a method for scaling the network size that preserves first- and second-order statistics, building on existing work on network theory. Our new implementation enabled the use of more detailed neuron models with multicompartmental morphologies and multiple biophysically realistic ion channels. This opens the model to new research, including the study of dendritic processing, the influence of individual channel parameters, the relation to local field potentials, and other multiscale interactions. The scaling method we used provides flexibility to increase or decrease the network size as needed when running these CPU-intensive detailed simulations. Finally, NetPyNE facilitates modifying or extending the model using its declarative language; optimizing model parameters; running efficient, large-scale parallelized simulations; and analyzing the model through built-in methods, including local field potential calculation and information flow measures.

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