scholarly journals Probabilistic continuity of a pullback random attractor in time-sample

2020 ◽  
Vol 25 (7) ◽  
pp. 2699-2772
Author(s):  
Shulin Wang ◽  
◽  
Yangrong Li ◽  
Keyword(s):  
Random Attractor ◽  
Time Sample

scholarly journals Random attractor for a stochastic viscous coupled Camassa-Holm equation

2013 ◽  
Vol 2013 (1) ◽  
pp. 201
Author(s):  
Zhehao Huang ◽  
Hao Tang ◽  
Zhengrong Liu
Keyword(s):  
Random Attractor ◽  
Holm Equation

Real-Time Sample Confirmation with Wireless Acoustic Technology During Downhole Sampling

2016 ◽  
Author(s):  
Antônio Mataruco ◽  
Lauren Harner ◽  
Leonardo Castellões
Keyword(s):  
Real Time ◽  
Time Sample

scholarly journals Existence of Random Attractors for ap-Laplacian-Type Equation with Additive Noise

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Wenqiang Zhao ◽  
Yangrong Li
Keyword(s):  
Dynamical System ◽  
Additive Noise ◽  
Single Point ◽  
Type Equation ◽  
Random Attractor ◽  
Approximation Procedure ◽  
Restrictive Assumption ◽  
Stochastic Dynamical System ◽  
Additive White Noise ◽  
Uniqueness Of A Solution

We first establish the existence and uniqueness of a solution for a stochasticp-Laplacian-type equation with additive white noise and show that the unique solution generates a stochastic dynamical system. By using the Dirichlet forms of Laplacian and an approximation procedure, the nonlinear obstacle, arising from the additive noise is overcome when we make energy estimate. Then, we obtain a random attractor for this stochastic dynamical system. Finally, under a restrictive assumption on the monotonicity coefficient, we find that the random attractor consists of a single point, and therefore the system possesses a unique stationary solution.

scholarly journals Upper Semicontinuity of Random Attractors for Nonautonomous Stochastic Reversible Selkov System with Multiplicative Noise

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Chunxiao Guo ◽  
Yanfeng Guo ◽  
Xiaohan Li
Keyword(s):  
Multiplicative Noise ◽  
Upper Semicontinuity ◽  
Random Attractor ◽  
Main Difficulty ◽  
Asymptotic Compactness ◽  
Random Attractors

In this paper, the existence of random attractors for nonautonomous stochastic reversible Selkov system with multiplicative noise has been proved through Ornstein-Uhlenbeck transformation. Furthermore, the upper semicontinuity of random attractors is discussed when the intensity of noise approaches zero. The main difficulty is to prove the asymptotic compactness for establishing the existence of tempered pullback random attractor.

2‐D wavepath migration

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1528-1537 ◽  
Author(s):  
H. Sun ◽  
G. T. Schuster
Keyword(s):  
Fresnel Zone ◽  
Complex Structure ◽  
Computation Time ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Kirchhoff Migration ◽  
Time Sample ◽  
Grid Points ◽  
Computationally Intensive ◽  
Single Trace

Prestack Kirchhoff migration (KM) is computationally intensive for iterative velocity analysis. This is partly because each time sample in a trace must be smeared along a quasi‐ellipsoid in the model. As a less costly alternative, we use the stationary phase approximation to the KM integral so that the time sample is smeared along a small Fresnel zone portion of the quasi‐ellipsoid. This is equivalent to smearing the time samples in a trace over a 1.5‐D fat ray (i.e., wavepath), so we call this “wavepath migration” (WM). This compares to standard KM, which smears the energy in a trace along a 3‐D volume of quasi‐concentric ellipsoids. In principle, single trace migration with WM has a computational count of [Formula: see text] compared to KM, which has a computational count of [Formula: see text], where N is the number of grid points along one side of a cubic velocity model. Our results with poststack data show that WM produces an image that in some places contains fewer migration artifacts and is about as well resolved as the KM image. For a 2‐D poststack migration example, the computation time of WM is less than one‐third that of KM. Our results with prestack data show that WM images contain fewer migration artifacts and can define the complex structure more accurately. It is also shown that WM can be significantly faster than KM if a slant stack technique is used in the migration. The drawback with WM is that it is sometimes less robust than KM because of its sensitivity to errors in estimating the incidence angles of the reflections.

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