Conservative Continuous-Stage Stochastic Runge–Kutta Methods for Stochastic Differential Equations by Xiuyan Li, Zhenyu Wang, Qiang Ma, Xiaohua Ding

Subjects: “…stochastic differential equations…”
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The mean field limit of stochastic differential equation systems modelling grid cells by Carrillo, JA, Clini, A, Solem, S

Second weak order explicit stabilized methods for stiff stochastic differential equations by Abdulle, A, Vilmart, G, Zygalakis, K

“…We introduce a new family of explicit integrators for stiff Itˆo stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of onestep stabilized methods with extended stability domains and do not suffer from stepsize reduction that standard explicit methods face. …”

Optimal decisions: From neural spikes, through stochastic differential equations, to behavior by Holmes, P, Shea-Brown, E, Moehlis, J, Bogacz, R, Gao, J, Aston-Jones, G, Clayton, E, Rajkowski, J, Cohen, J

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. …”

An improved two-step method in stochastic differential equation's structural parameter estimation by Abd. Rahman, Haliza

“…Regression spline characterised by the truncated power series basis with Bayesian approach is considered in the first step of a two-step method for estimating the structural parameters for stochastic differential equation (SDE). Previous methodology revealed the selection of knot and order of spline can be done heuristically based on a scatter plot. …”
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Application of stochastic differential equations and stochastic delay differential equations in population dynamics by Bahar, Arifah

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Modification of two-step method in estimating the parameters of stochastic differential equation models by Lazim, N. H. M., Rahman, H. A., Bahar, A.

“…Two-step method is introduced as an alternative method to classical methods in estimating the drift and diffusion parameters of the Stochastic Differential Equations (SDEs) models. Previous studies indicated that this method provides high percentage of accuracy of the estimated diffusion parameter of Lotka-Volterra model with simulated data. …”

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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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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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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RETRACTED ARTICLE: Anticipated backward doubly stochastic differential equations with non-Liphschitz coefficients by Aidara Sadibou

Subjects: “…anticipated backward doubly stochastic differential equation…”
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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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