منابع مشابه
Stability of Ordinary Differential Equations with Colored Noise Forcing
We present a perturbation method for determining the moment stability of linear ordinary differential equations with parametric forcing by colored noise. In particular, the forcing arises from passing white noise through an nth order filter. We carry out a perturbation analysis based on a small parameter ε that gives the amplitude of the forcing. Our perturbation analysis is based on a ladder o...
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Different from the system in classical mathematics, a Smarandache system is a contradictory system in which an axiom behaves in at least two different ways within the same system, i.e., validated and invalided, or only invalided but in multiple distinct ways. Such systems exist extensively in the world, particularly, in our daily life. In this paper, we discuss such a kind of Smarandache system...
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The diierential equation dx(t) = a(x(t); t) dZ (t) + b(x(t); t) dt for fractal-type functions Z (t) is determined via fractional calculus. Under appropriate conditions we prove existence and uniqueness of a local solution by means of its representation x(t) = h(y(t) +Z(t); t) for certain C 1-functions h and y. The method is also applied to It^ o stochastic diierential equations and leads to a g...
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ژورنال
عنوان ژورنال: SIAM Journal on Control and Optimization
سال: 2013
ISSN: 0363-0129,1095-7138
DOI: 10.1137/110855302