Large and small deviations of a string driven by a two-parameter Gaussian noise white in time

2003 ◽  
Vol 40 (04) ◽  
pp. 946-960
Author(s):  
Peter Caithamer
Keyword(s):  
Large Deviations ◽  
Lower Bounds ◽  
Gaussian Noise ◽  
Spatial Covariance ◽  
Small Deviations ◽  
One Dimensional ◽  
Two Parameter

Upper as well as lower bounds for both the large deviations and small deviations of several sup-norms associated with the displacements of a one-dimensional string driven by a Gaussian noise which is white in time and has general spatial covariance are developed.

Large and small deviations of a string driven by a two-parameter Gaussian noise white in time

2003 ◽  
Vol 40 (4) ◽  
pp. 946-960 ◽  
Author(s):  
Peter Caithamer
Keyword(s):  
Large Deviations ◽  
Lower Bounds ◽  
Gaussian Noise ◽  
Spatial Covariance ◽  
Small Deviations ◽  
One Dimensional ◽  
Two Parameter

Upper as well as lower bounds for both the large deviations and small deviations of several sup-norms associated with the displacements of a one-dimensional string driven by a Gaussian noise which is white in time and has general spatial covariance are developed.

Energy of a string driven by a two-parameter Gaussian noise white in time

2001 ◽  
Vol 38 (04) ◽  
pp. 960-974 ◽  
Author(s):  
Boris P. Belinskiy ◽  
Peter Caithamer
Keyword(s):  
Wave Equation ◽  
Gaussian Noise ◽  
Spatial Dimension ◽  
Spatial Covariance ◽  
Stochastic Wave Equation ◽  
Two Parameter

In this paper we consider the stochastic wave equation in one spatial dimension driven by a two-parameter Gaussian noise which is white in time and has general spatial covariance. We give conditions on the spatial covariance of the driving noise sufficient for the string to have finite expected energy and calculate this energy as a function of time. We show that these same conditions on the spatial covariance of the driving noise are also sufficient to guarantee that the energy of the string has a version which is continuous almost surely.

Energy of a string driven by a two-parameter Gaussian noise white in time

2001 ◽  
Vol 38 (4) ◽  
pp. 960-974 ◽  
Author(s):  
Boris P. Belinskiy ◽  
Peter Caithamer
Keyword(s):  
Wave Equation ◽  
Gaussian Noise ◽  
Spatial Dimension ◽  
Spatial Covariance ◽  
Stochastic Wave Equation ◽  
Two Parameter

In this paper we consider the stochastic wave equation in one spatial dimension driven by a two-parameter Gaussian noise which is white in time and has general spatial covariance. We give conditions on the spatial covariance of the driving noise sufficient for the string to have finite expected energy and calculate this energy as a function of time. We show that these same conditions on the spatial covariance of the driving noise are also sufficient to guarantee that the energy of the string has a version which is continuous almost surely.

On Approximate Large Deviations for 1D Diffusion

2003 ◽  
Vol 10 (2) ◽  
pp. 381-399
Author(s):  
A. Yu. Veretennikov
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Large Deviations ◽  
Stochastic Differential Equation ◽  
Approximation Scheme ◽  
Sufficient Conditions ◽  
Rate Function ◽  
Euler Approximation ◽  
One Dimensional

Abstract We establish sufficient conditions under which the rate function for the Euler approximation scheme for a solution of a one-dimensional stochastic differential equation on the torus is close to that for an exact solution of this equation.

Lower Bounds to the Eigenvalues in One-Dimensional Problems by a Shift in the Weight Function

1970 ◽  
Vol 37 (2) ◽  
pp. 267-270 ◽  
Author(s):  
D. Pnueli
Keyword(s):  
Lower Bound ◽  
Weight Function ◽  
Lower Bounds ◽  
Variational Formulation ◽  
Ritz Method ◽  
The Other ◽  
One Dimensional ◽  
Systematic Shift ◽  
The One ◽  
Detailed Computation

A method is presented to obtain both upper and lower bound to eigenvalues when a variational formulation of the problem exists. The method consists of a systematic shift in the weight function. A detailed procedure is offered for one-dimensional problems, which makes improvement of the bounds possible, and which involves the same order of detailed computation as the Rayleigh-Ritz method. The main contribution of this method is that it yields the “other bound;” i.e., the one which cannot be obtained by the Rayleigh-Ritz method.

Lower Bounds for Large Deviations inRd,d > 1

1991 ◽  
Vol 154 (1) ◽  
pp. 41-49 ◽  
Author(s):  
A. V. Nagaev
Keyword(s):  
Large Deviations ◽  
Lower Bounds

scholarly journals Upper and lower bounds on the speed of a one-dimensional excited random walk

2019 ◽  
Vol 12 (1) ◽  
pp. 97-115
Author(s):  
Erin Madden ◽  
Brian Kidd ◽  
Owen Levin ◽  
Jonathon Peterson ◽  
Jacob Smith ◽  
...  
Keyword(s):  
Random Walk ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
One Dimensional ◽  
Excited Random Walk

Upper and Lower Bounds for the Parameters of One-Dimensional Theories for Sandwich Fracture Specimens

2020 ◽  
Vol 88 (3) ◽  
Author(s):  
Roberta Massabò
Keyword(s):  
Crack Length ◽  
Lower Bounds ◽  
Beam Theory ◽  
Approximate Solutions ◽  
Upper And Lower Bounds ◽  
Model Parameters ◽  
One Dimensional ◽  
Limit Value ◽  
Elastic Mismatch ◽  
Fracture Specimens

Abstract Upper and lower bounds for the parameters of one-dimensional theories used in the analysis of sandwich fracture specimens are derived by matching the energy release rate with two-dimensional elasticity solutions. The theory of a beam on an elastic foundation and modified beam theory are considered. Bounds are derived analytically for foundation modulus and crack length correction in single cantilever beam (SCB) sandwich specimens and verified using accurate finite element results and experimental data from the literature. Foundation modulus and crack length correction depend on the elastic mismatch between face sheets and core and are independent of the core thickness if this is above a limit value, which also depends on the elastic mismatch. The results in this paper clarify conflicting results in the literature, explain the approximate solutions, and highlight their limitations. The bounds of the model parameters can be applied directly to specimens satisfying specific geometrical/material ratios, which are given in the paper, or used to support and validate numerical calculations and define asymptotic limits.

scholarly journals Localization for the one-dimensional Anderson model via positivity and large deviations for the Lyapunov exponent

2019 ◽  
Vol 372 (5) ◽  
pp. 3619-3667 ◽  
Author(s):  
Valmir Bucaj ◽  
David Damanik ◽  
Jake Fillman ◽  
Vitaly Gerbuz ◽  
Tom VandenBoom ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Large Deviations ◽  
Anderson Model ◽  
One Dimensional ◽  
The One
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