Results 261 to 270 of about 13,470 (307)

Stochastic stabilisation of functional differential equations

Systems & Control Letters, 2005
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John A. D. Appleby, Xuerong Mao
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Perturbed Nonlocal Stochastic Functional Differential Equations

Qualitative Theory of Dynamical Systems, 2020
The authors discuss the asymptotic behavior of the solution for a class of perturbed nonlocal stochastic functional differential equations. They evaluate the distance between the latter and of the unperturbed solution, in finite time-intervals, and on maximal intervals as the small perturbations tend to zero. These results non-trivially extend previous
Zhang, Qi, Ren, Yong
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Existence–uniqueness and continuation theorems for stochastic functional differential equations [PDF]

Journal of Differential Equations, 2008
The main aim of this paper is to develop some basic theories of stochastic functional differential equations (SFDEs). Firstly, we establish stochastic versions of the well-known Picard local existence–uniqueness theorem given by Driver and continuation ...
Daoyi Xu, Zhiguo Yang
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Stochastic suppression and stabilization of functional differential equations

Systems & Control Letters, 2010
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Fuke Wu, Xuerong Mao, Shigeng Hu
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Stability of hybrid stochastic functional differential equations

Applied Mathematics and Computation, 2019
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Dehao Ruan, Liping Xu, Jiaowan Luo
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Stability of stochastic functional differential equations

1992
Here we will consider the Ito type SRDE $$\left. {\begin{array}{*{20}{c}} {dx\left( t \right) = {a_1}\left( {t,{x_t}} \right)dt + {a_2}\left( {t,{x_t}} \right)d\xi \left( t \right),{\kern 1pt} t \geqslant {t_0},} \\ {{x_t}\left( \theta \right) = x\left( {t + \theta } \right),{\kern 1pt} - h \leqslant \theta \leqslant 0,{\kern 1pt} x:{J_x} \to {R^n}.
V. Kolmanovskii, A. Myshkis
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Stochastic Comparison of Solutions of Stochastic Functional Differential Equations

Zeitschrift für Analysis und ihre Anwendungen, 2007
A stochastic comparison of solutions of nonlinear stochastic functional differential equations with different drift and diffusion coefficients is obtained. Some known results are generalized.
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Stability of stochastic functional differential equations

Journal of Mathematical Physics, 1974
A system of functional differential equations with random retardation, ẋ(t) = f(t, xt), is studied, where xt(θ) = x(t + θ), η(t, ω) ≤ θ ≤ 0, − r ≤ η(t, ω) ≤ 0, and η(t, ω) is a stochastic process defined on some probability space (Ω, μ, P). Some comparison theorems are stated and proved in details under suitable assumptions on f(t, xt).
Chang, M. H., Ladde, G., Liu, P. T.
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Stability analysis of impulsive stochastic functional differential equations

Communications in Nonlinear Science and Numerical Simulation, 2020
In this paper, the authors use the Razumikhin techniques and Lyapunov functions to investigate the stability of impulsive stochastic functional differential equations. The results show that impulses make contribution to the exponential stability of stochastic differential systems with any time delay even they are unstable.
Yingxin Guo, Quanxin Zhu, Fei Wang
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Functional Formulation of Stochastic Differential Equations

2020
This section casts stochastic dynamics into the previously developed language of field theory. The resulting formulation is advantageous in several respects. First, it expresses the dynamical equations into a path-integral, where the dynamic equations give rise to the definition of an “action.” In this way, the perturbation expansion with the help of ...
Moritz Helias, David Dahmen
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