Results 241 to 250 of about 150,474 (283)

Quasi Contraction of Stochastic Functional Differential Equations

Journal of Partial Differential Equations, 2023
Summary: Using a novel approach, we present explicit criteria for the quasi contraction of stochastic functional differential equations. As an application, some sufficient conditions ensuring the contraction property of the solution to the considered equations are obtained. Finally, some examples are investigated to illustrate the theory.
Zhao, Jiaxin, Li, Zhi, Xu, Liping
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Perturbed Impulsive Neutral Stochastic Functional Differential Equations

Qualitative Theory of Dynamical Systems, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cheng, Lijuan, Hu, Lanying, Ren, Yong
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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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Functionally perturbed stochastic differential equations

Mathematische Nachrichten, 2006
AbstractThis paper is devoted to the large class of stochastic differential equations of the Ito type whose coefficients are functionally perturbed and depend on a small parameter. The solution of a such equation is compared with the solution of the corresponding unperturbed equation, in the (2m)‐th moment sense, on finite intervals or on intervals ...
Miljana Jovanović, Svetlana Janković
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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 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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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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Stochastic stabilisation of functional differential equations

Systems & Control Letters, 2005
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Appleby, John A. D., Mao, Xuerong
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Fast-slow-coupled stochastic functional differential equations

Journal of Differential Equations, 2022
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Fuke Wu, George Yin
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