On the Exponential Stability of Stochastic Differential Equations

By Hong-ke Wang. International Conference of Fuzzy Information and Engineering, 2009

309 citations recorded by the source corpus.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/004da7f30997d34798ab5752e9740099232ff375

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Citations in the corpus

Stochastic population dynamics under regime switching II (2007, background): “4) may explode to infinity at a finite time [17,18,20].”
Stochastic functional differential equations with infinite delay driven by G‐Brownian motion (2013, methodology): “We refer the reader to Mao [1, 2] and the references therein for a wealth of reference materials on the subject.”
The partially truncated Euler–Maruyama method and its stability and boundedness (2017, unknown): “, [13, 16, 17]) that the scalar stochastic differential equation (SDE) dx(t) = − ( x(t) + x(5)(t) ) dt+ x(2)(t)dB(t), t ≥ 0, (1.”
A Stochastic Differential Equation SIS Epidemic Model (2011, background): “[23, 24, 25]) that for any given initial value S0 ∈ (0, N) there is a unique maximal local solution I(t) on t ∈ [0, τe), where τe is the explosion time.”
Asymptotic Stability of Stochastic Differential Equations Driven by Lévy Noise (2009, background): “The extension to nonlinear SDEs driven by continuous semimartingales and also to stochastic delay and more general stochastic functional differential equations has been extensively studied by Mao in a series of books and articles (see [13], [14], [16], and the references therein).”
Asymptotic stability of impulsive stochastic partial differential equations with infinite delays (2009, unknown): “The stability investigation of stochastic differential equations with delays have been discussed by several authors [5,9,12,14,15,19,22].”
Lyapunov-type conditions and stochastic differential equations driven by $G$-Brownian motion (2014, methodology): “We recall Has’minskǐi [6] and Mao [11] for details in this topic for SDEs.”
Existence–uniqueness and continuation theorems for stochastic functional differential equations (2008, unknown): “Many important results can be found in [1–19] and references cited therein.”
The SIS epidemic model with Markovian switching (2012, unknown): “[11, 15, 25, 26, 28, 34, 36]).”
Stochastic Population Systems (2009, background): “Since the coefficients of the equation are locally Lipschitz continuous, for any given initial value x 0 ∈ n +, there is a unique maximal local solution x t on t ∈ 0 e , where e is the explosion time (see [18, 21]).”