High order weak methods for stochastic differential equations based on modified equations by Abdulle, A, Cohen, D, Vilmart, G, Zygalakis, K

“…Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new high order weak methods, in particular, implicit integrators well suited for stiff stochastic problems, and integrators that exactly conserve all quadratic first integrals of a stochastic dynamical system. …”

Application of stochastic differential equations and stochastic delay differential equations in population dynamics by Bahar, Arifah

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Applications of stochastic differential equations and stochastic delay differential equations in population dynamics [microfilm] /

Theory of stochastic differential equations with jumps and applications : mathematical and analytical techniques with applications to engineering / by 230389 Situ, Rong

Subjects: “…Stochastic differential equations…”

Stability Analysis of Explicit and Implicit Stochastic Runge-Kutta Methods for Stochastic Differential Equations by Adam, Samsudin, Norhayati, Rosli, Amalina Nisa, Ariffin

“…The stability analysis of the schemes in mean-square norm is investigated. Linear stochastic differential equations are used as test equations to demonstrate the efficiency of the proposed schemes.…”
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Stability analysis of explicit and semi-implicit derivative-free methods for stochastic differential equations by Norhayati, Rosli, Noor Amalina Nisa, Ariffin

“…This paper is devoted to investigate the mean-square stability of explicit and semi-implicit derivative-free methods to a class of stochastic differential equations (SDEs). The mean-square stability functions and regions of explicit and semi-implicit numerical approximation schemes are obtained for a linear stochastic differential equation with multiplicative noise. …”
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Comparative study of stochastic Taylor methods and derivative-free methods for stochastic differential equations by Muhammad Fahmi, Ahmad Zuber, Norhayati, Rosli

“…However, modelling these systems using deterministic model such as ODEs is inadequate as the system is subjected to the uncontrolled factors of environmental noise. Stochastic differential equations (SDEs) which are originating from the irregular Brownian motion can be applied to model such systems that subjected to the uncontrolled factors of noisy behaviour. …”
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Exact Coupling Method for Stratonovich Stochastic Differential Equation Using Non-Degeneracy for the Diffusion by Yousef Alnafisah

Subjects: “…Stochastic differential equation…”
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Existence and Stability of Solutions of Fuzzy Fractional Stochastic Differential Equations with Fractional Brownian Motions by Elhoussain Arhrrabi, M’hamed Elomari, Said Melliani, Lalla Saadia Chadli

“…The existence, uniqueness, and stability of solutions to fuzzy fractional stochastic differential equations (FFSDEs) driven by a fractional Brownian motion (fBm) with the Lipschitzian condition are investigated. …”
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Estimates for the difference between approximate and exact solutions to stochastic differential equations in the G-framework by Faiz Faizullah, Ilyas Khan, Mukhtar M. Salah, Ziyad Ali Alhussain

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Convergence of Relative Entropy for Euler–Maruyama Scheme to Stochastic Differential Equations with Additive Noise by Yuan Yu

“…For a family of stochastic differential equations driven by additive Gaussian noise, we study the asymptotic behaviors of its corresponding Euler–Maruyama scheme by deriving its convergence rate in terms of relative entropy. …”
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Adopting Feynman–Kac Formula in Stochastic Differential Equations with (Sub-)Fractional Brownian Motion by Bodo Herzog

“…The aim of this work is to establish and generalize a relationship between fractional partial differential equations (fPDEs) and stochastic differential equations (SDEs) to a wider class of stochastic processes, including fractional Brownian motions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><msubsup><mi>B</mi><mi>t</mi><mi>H</mi></msubsup><mo>,</mo><mi>t</mi><mo>≥</mo><mn>0</mn><mo>}</mo></mrow></semantics></math></inline-formula> and sub-fractional Brownian motions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><msubsup><mi>ξ</mi><mi>t</mi><mi>H</mi></msubsup><mo>,</mo><mi>t</mi><mo>≥</mo><mn>0</mn><mo>}</mo></mrow></semantics></math></inline-formula> with Hurst parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mo>∈</mo><mo>(</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>. …”
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INTERVAL PREDICTION OF NON-STATIONARY PROCESSES, DESCRIBED BY STOCHASTIC DIFFERENTIAL EQUATIONS WITH VARIABLE PARAMETERS by A. V. Ausiannikau

“…The task of interval prediction of non-stationary processes of stochastic differential equations described by models with variable parameters is considered. …”
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Strong uniqueness of solutions of stochastic differential equations with jumps and non-Lipschitz random coefficients by G. Kulinich, S. Kushnirenko

Subjects: “…Stochastic differential equations…”
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Correction: Sobolev-type nonlinear Hilfer fractional stochastic differential equations with noninstantaneous impulsive by Mohamed Adel, M. Elsaid Ramadan, Hijaz Ahmad, Thongchai Botmart

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Stabilization of Stochastic Differential Equations Driven by G-Brownian Motion with Aperiodically Intermittent Control by Pengju Duan

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The Analytic solution for some non-linear stochastic differential equation by linearization (Linear-transform) by Abdulghafoor J. Salim, Nibal Abdulrhman

Subjects: “…stochastic differential equation…”
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Sufficient Conditions on the Exponential Stability of Neutral Stochastic Differential Equations with Time-Varying Delays by Yanwei Tian, Baofeng Chen

“…The exponential stability is investigated for neutral stochastic differential equations with time-varying delays. Based on the Lyapunov stability theory and linear matrix inequalities (LMIs) technique, some delay-dependent criteria are established to guarantee the exponential stability in almost sure sense. …”
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Entropy Dissipation for Degenerate Stochastic Differential Equations via Sub-Riemannian Density Manifold by Qi Feng, Wuchen Li

“…We studied the dynamical behaviors of degenerate stochastic differential equations (SDEs). We selected an auxiliary Fisher information functional as the Lyapunov functional. …”
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Parameter Estimation of Population Pharmacokinetic Models with Stochastic Differential Equations: Implementation of an Estimation Algorithm by Fang-Rong Yan, Ping Zhang, Jun-Lin Liu, Yu-Xi Tao, Xiao Lin, Tao Lu, Jin-Guan Lin

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