Simulation of radiation belt wave-particle interactions in an MHD-particle framework by Anthony A. Chan, Scot R. Elkington, William J. Longley, William J. Longley, Suhail A. Aldhurais, Suhail A. Aldhurais, Suhail A. Aldhurais, Shah S. Alam, Jay M. Albert, Allison N. Jaynes, David M. Malaspina, David M. Malaspina, Qianli Ma, Wen Li

“…Simulation of local acceleration and pitch-angle scattering due to cyclotron-scale interactions is incorporated by including stochastic differential equation (SDE) methods in the MHD-particle framework. …”
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Stochastic neural field models of binocular rivalry waves by Webber, M

“…By regarding the motion of a stochastic travelling wave as being made up of two distinct components, firstly, the drift-diffusion of its overall position, secondly, fast fluctuations in its shape around some average front shape, we are able to derive a stochastic differential equation for the front position with respect to time. …”

Continuous Time Autoregressive Moving Average Processes Driven by Semi-Levy Process by Navideh Modarresi, Saeid Rezakhah, Shirin Shoaee

“…The Levy-driven CARMA process described as the unique solution of some stochastic differential equation [5].  It is known that these family of CARMA processes are stationary or asymptotic stationary. …”
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Calculation and Management of Premium Funds in Sharia Insurance based on Langevin Type Model of Return on Investment by Khusnul Khotimah, Mahmudi Mahmudi, Nina Fitriyati

“…Keywords: Langevin type model, stochastic differential equation, system without a saving element, Al-Mudharabah principle, Monte–Carlo simulation.   …”
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Finite Iterative Forecasting Model Based on Fractional Generalized Pareto Motion by Wanqing Song, Shouwu Duan, Dongdong Chen, Enrico Zio, Wenduan Yan, Fan Cai

“…An iterative prediction model is obtained from the Langevin-type stochastic differential equation driven by fGPm. The prediction model inherits the LRD condition <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mo>></mo><mn>1</mn><mo>⁄</mo><mi>α</mi></mrow></semantics></math></inline-formula> of fGPm and the time series, simulated by the Monte Carlo method, shows the superiority of the prediction model to predict data with high jumps. …”
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A Note on Causation versus Correlation in an Extreme Situation by X. San Liang, Xiu-Qun Yang

“…By slightly perturbing the system with some noise, solving a stochastic differential equation, and letting the perturbation go to zero, it can be shown that <inline-formula><mjx-container class="MathJax CtxtMenu_Attached_0" jax="CHTML" style="font-size: 113.1%; position: relative;" role="presentation" tabindex="0" ctxtmenu_counter="5"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-semantics><mjx-msub><mjx-mi class="mjx-i" noic="true"><mjx-c class="mjx-c1D70F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.153em;"><mjx-mrow size="s"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D434 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c2192"></mjx-c></mjx-mo><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D435 TEX-I"></mjx-c></mjx-mi></mjx-mrow></mjx-script></mjx-msub></mjx-semantics></mjx-math><mjx-assistive-mml role="presentation" unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mrow><mi>A</mi><mo>→</mo><mi>B</mi></mrow></msub></semantics></math></mjx-assistive-mml></mjx-container></inline-formula> approaches 100%, just as one would have expected.…”
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Principles of equity valuation / by Davidson, Ian, 1949-, Tippett, Mark, 1949-

“…Introduction -- The measurement of returns on bonds, equities and other financial instruments -- The relationship between risk and return -- Alternative approaches to the relationship between risk and return -- Returns and the capital structure of the firm -- The relationship between equity value, dividends and other cash flow streams -- The relationship between book (accounting) rates of return and the cost of capital for firms and capital projects -- Statistical foundations : first order stochastic differential equations -- Statistical foundations : systems of and higher order stochastic differential equations -- Equity valuation : a canonical model -- Equity valuation : non-linearities and scaling -- Equity valuation : multi-variable investment opportunity sets -- Equity valuation : higher order investment opportunity sets, momentum and acceleration.…”

Parabolic equations and diffusion processes with divergence-free vector fields by Xi, G

“…The stochastic Lagrangian formulation to the Navier-Stokes equations is described by stochastic differential equations, which essentially represent the diffusions under divergence-free velocity fields. …”

Stochastic optimal control for dynamics of forward backward doubly SDEs of mean-field type by Nassima Berrouis, Boulakhras Gherbal, Abdelhakim Ninouh

“… In this paper we establish in first the existence of strong optimal solutions of a control problem for dynamics driven by a linear forward-backward doubly stochastic differential equations of mean-field type (MF-FBDSDEs), with random coefficients and non linear functional cost. …”
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Semi-implicit Taylor schemes for stiff rough differential equations by Riedel, S, Wu, Yue

“…We study a class of semi-implicit Taylor-type numerical methods that are easy to implement and designed to solve multidimensional stochastic differential equations driven by a general rough noise, e.g. a fractional Brownian motion. …”

Numerical Stabilities of Vasicek and Geometric Brownian Motion Models by O. C. Badibi, I. Ramadhani, M. A. Ndondo, S. D. Kumwimba

“…Stochastic differential equations (SDEs) are very often used as models for a large number of phenomena in the physical, economic and management sciences. …”
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Stabilisation in distribution of hybrid ordinary differential equations by periodic noise by Arifah Bahar, Ran Dong, Xuerong Mao

“…Periodic hybrid stochastic differential equations are often used to model them. …”
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Stabilisation in distribution of hybrid ordinary differential equations by periodic noise. by Bahar, Arifah, Dong, Ran, Mao, Xuerong

“…Periodic hybrid stochastic differential equations are often used to model them. …”
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Jump Models with Delay—Option Pricing and Logarithmic Euler–Maruyama Scheme by Nishant Agrawal, Yaozhong Hu

“…In this paper, we obtain the existence, uniqueness, and positivity of the solution to delayed stochastic differential equations with jumps. This equation is then applied to model the price movement of the risky asset in a financial market and the Black–Scholes formula for the price of European option is obtained together with the hedging portfolios. …”
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Leader-Follower Formation Control of Uncertain USV Networks under Stochastic Disturbances by Ali Azarbahram, Naser Pariz, Mohammad Bagher Naghibi-Sistani, Reihaneh Kardehi Moghaddam

“…A comprehensive model including kinematics and kinetics of each USV agent is then derived as stochastic differential equations including standard Wiener processes. …”
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A stochastic hybrid systems based framework for modeling dependent failure processes. by Mengfei Fan, Zhiguo Zeng, Enrico Zio, Rui Kang, Ying Chen

“…The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. …”
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Anticipating random periodic solutions I: SDEs with multiplicative linear noise by Feng, C, Wu, Y, Zhao, H

“…In this paper, we study the existence of random periodic solutions for semilinear stochastic differential equations. We identify them as solutions of coupled forward–backward infinite horizon stochastic integral equations (IHSIEs), using the “substitution theorem” of stochastic differential equations with anticipating initial conditions. …”

Assessment of Information predictability of stochastic processes by A. V. Ausiannikau

“…We consider examples of algorithms for estimating the predictability of information for the processes described by the optimal difference schemes, equivalent prognostic models in the form of stochastic differential equations.…”
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On Random Dynamical Systems Generated by White Noise Time Change of Deterministic Dynamical Systems by Mohamed Hmissi, Farida Mokchaha

“…We prove that the obtained random dynamical systems are solutions of some stochastic differential equations whenever the deterministic dynamical systems are solutions of ordinary differential equations.…”
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Backward stochastic dynamics on a filtered probability space by Liang, G, Lyons, T, Qian, Z

“…We demonstrate that backward stochastic differential equations (BSDE) may be reformulated as ordinary functional differential equations on certain path spaces. …”