# Stochastic Stability of Damped Mathieu Oscillator Parametrically Excited by a Gaussian Noise

## Related Articles

- Nonequilibrium Thermal Dynamic Modeling of Porous Medium Vacuum Drying Process. Zhijun Zhang; Ninghua Kong // Mathematical Problems in Engineering;2012, Vol. 2012, Special section p1
Porous medium vacuum drying is a complicated heat and mass transfer process. Based on the theory of heat and mass transfer, a coupled model for the porous medium vacuum drying process is constructed. The model is implemented and solved using COMSOL software. The water evaporation rate is...

- Stochastic Stability of Damped Mathieu Oscillator Parametrically Excited by a Gaussian Noise. Floris, Claudio // Mathematical Problems in Engineering;2012, Vol. 2012, Special section p1
This paper analyzes the stochastic stability of a damped Mathieu oscillator subjected to a parametric excitation of the form of a stationary Gaussian process, which may be both white and coloured. By applying deterministic and stochastic averaging, two Ito's differential equations are retrieved....

- Short-Range Spin Glasses and Random Overlap Structures. Arguin, Louis-Pierre; Damron, Michael // Journal of Statistical Physics;Apr2011, Vol. 143 Issue 2, p226
Properties of Random Overlap Structures (ROSt)'s constructed from the Edwards-Anderson (EA) Spin Glass model on â„¤ with periodic boundary conditions are studied. ROSt's are â„•Ã—â„• random matrices whose entries are the overlaps of spin configurations sampled from the Gibbs...

- Processes of normal inverse Gaussian type. Barndorff-Nielsen, Ole E. // Finance & Stochastics;1998, Vol. 2 Issue 1, p41
With the aim of modelling key stylized features of observational series from finance and turbulence a number of stochastic processes with normal inverse Gaussian marginals and various types of dependence structures are discussed. Omstein-Uhlenbeck type processes, superpositions of such processes...

- Pair formation. Hadeler, K. // Journal of Mathematical Biology;Mar2012, Vol. 64 Issue 4, p613
A multitype pair formation model for a one-sex population, without separation, with given type distribution of singles, produces a distribution of pairs with the given type distribution as a marginal distribution. The pair distribution can be seen as a nonnegative symmetric matrix. For this...

- Large n Limit of Gaussian Random Matrices with External Source, Part III: Double Scaling Limit. Bleher, Pavel; Kuijlaars, Arno // Communications in Mathematical Physics;Feb2007, Vol. 270 Issue 2, p481
We consider the double scaling limit in the random matrix ensemble with an external source defined on n ï¿½ n Hermitian matrices, where A is a diagonal matrix with two eigenvalues ï¿½ a of equal multiplicities. The value a = 1 is critical since the eigenvalues of M accumulate as n ? 8 on...

- Invariant Gaussian measures for operators on Banach spaces and linear dynamics. Bayart, Frédéric; Grivaux, Sophie // Proceedings of the London Mathematical Society;2007, Vol. 94 Issue 1, p181
We give conditions for an operator T on a complex separable Banach space X with sufficiently many eigenvectors associated to eigenvalues of modulus 1 to admit a non-degenerate invariant Gaussian measure with respect to which it is weak-mixing. The existence of such a measure depends on the...

- A Monte Carlo method for computing the marginal likelihood in nondecomposable Gaussian graphical models. ATAY-KAYIS, ALIYE; MASSAM, HÉLÈNE // Biometrika;Jun2005, Vol. 92 Issue 2, p317
A centred Gaussian model that is Markov with respect to an undirected graph G is characterised by the parameter set of its precision matrices which is the cone M+(G) of positive definite matrices with entries corresponding to the missing edges of G constrained to be equal to zero. In a Bayesian...

- Optimal rates of convergence for estimating Toeplitz covariance matrices. Cai, T.; Ren, Zhao; Zhou, Harrison // Probability Theory & Related Fields;Jun2013, Vol. 156 Issue 1/2, p101
Toeplitz covariance matrices are used in the analysis of stationary stochastic processes and a wide range of applications including radar imaging, target detection, speech recognition, and communications systems. In this paper, we consider optimal estimation of large Toeplitz covariance matrices...

- Gap probabilities in non-Hermitian random matrix theory. Akemann, G.; Phillips, M. J.; Shifrin, L. // Journal of Mathematical Physics;Jun2009, Vol. 50 Issue 6, p063504
We compute the gap probability that a circle of radius r around the origin contains exactly k complex eigenvalues. Four different ensembles of random matrices are considered: the Ginibre ensembles and their chiral complex counterparts, with both complex (Î²=2) or quaternion real (Î²=4)...