Monotonic Limit Properties for Solutions of BSDEs with Continuous Coefficients by ShengJun Fan, Xing Song, Ming Ma

“…This paper investigates the monotonic limit properties for the minimal and maximal solutions of certain one-dimensional backward stochastic differential equations with continuous coefficients.…”
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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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Existence and Uniqueness of Mild Solutions for Nonlinear Stochastic Impulsive Differential Equation by L. J. Shen, J. T. Sun

“…By using Schaefer's fixed theorem and stochastic analysis technique, we propose sufficient conditions on existence and uniqueness of solution for stochastic differential equations with impulses. An example is also discussed to illustrate the effectiveness of the obtained results.…”
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The Global Solutions and Moment Boundedness of Stochastic Multipantograph Equations by Maosheng Tian, Xuejing Meng, Jihong Chen, Xiaoqi Tang

“…Methods and techniques developed here have the potential to be applied in other unbounded delay stochastic differential equations.…”
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The Positive Role of Multiplicative Noise in Complete Synchronization of Unidirectionally Coupled Ring with Three Nodes by Yuzhu Xiao, Sufang Tang, Zhongkui Sun

“…Based on the theory of stochastic differential equations, we demonstrate that noise plays a positive role in complete synchronization. …”
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Pricing of European Currency Options with Uncertain Exchange Rate and Stochastic Interest Rates by Xiao Wang

“…Suppose that the interest rates obey stochastic differential equations, while the exchange rate follows an uncertain differential equation; this paper proposes a new currency model. …”
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Analytic Approximation of the Solutions of Stochastic Differential Delay Equations with Poisson Jump and Markovian Switching by Hua Yang, Feng Jiang

“…Most SDDEsPJMSs cannot be solved explicitly as stochastic differential equations. Therefore, numerical solutions have become an important issue in the study of SDDEsPJMSs. …”
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Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays by R. Sakthivel, P. Revathi, N. I. Mahmudov

“…We study the existence and asymptotic stability in pth moment of a mild solution to a class of nonlinear fractional neutral stochastic differential equations with infinite delays in Hilbert spaces. …”
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Solution theory of fractional SDEs in complete subcritical regimes by Lucio Galeati, Máté Gerencsér

“…We consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense. …”
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Multivalued Impulsive SDEs Driven by G-Brownian Noise: Periodic Averaging Result by Mahmoud Abouagwa, Anas D. Khalaf, Nadia Gul, Sultan Alyobi, Al-Sharef Mohamed

“…This paper aims to study two approximation theorems in view of the periodic averaging results for non-Lipschitz multivalued stochastic differential equations with impulses and G-Brownian motion (MISDEGs). …”
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Variable Step Size Adams Methods for BSDEs by Qiang Han

“…For backward stochastic differential equations (BSDEs), we construct variable step size Adams methods by means of Itô–Taylor expansion, and these schemes are nonlinear multistep schemes. …”
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Valuation of Credit Derivatives with Multiple Time Scales in the Intensity Model by Beom Jin Kim, Chan Yeol Park, Yong-Ki Ma

“…We propose approximate solutions for pricing zero-coupon defaultable bonds, credit default swap rates, and bond options based on the averaging principle of stochastic differential equations. We consider the intensity-based defaultable bond, where the volatility of the default intensity is driven by multiple time scales. …”
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Infinite Horizon Optimal Control of Stochastic Delay Evolution Equations in Hilbert Spaces by Xueping Zhu, Jianjun Zhou

“…The existence and uniqueness of the optimal control are obtained by means of associated infinite horizon backward stochastic differential equations without assuming the Gâteaux differentiability of the drift coefficient and the diffusion coefficient. …”
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A leaky integrate-and-fire model with adaptation for the generation of a spike train by Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Maria Francesca Carfora

“…We assume that adaptation is mainly due to a calcium-activated potassium current, and we consider two coupled stochastic differential equations for which an analytical approach combined with simulation techniques and numerical methods allow to obtain both qualitative and quantitative results about asymptotic mean firing rate, mean calcium concentration and the firing probability density. …”
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Moment Lyapunov exponent of delay differential equations by M. S. Fofana

“…We demonstrate this connection by studying the stability of perturbed deterministic and stochastic differential equations with fixed time delays in the displacement and derivative functions. …”
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A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and Distribution by D. P. Siu, G. S. Ladde

“…The system under investigation is a first-order linear nonhomogeneous system of Itô-Doob type stochastic differential equations with switching coefficients. …”
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Convertible Bonds with Higher Loan Rate: Model, Valuation, and Optimal Strategy by Haiyang Wang, Zhen Wu

“…We study the pricing problem for convertible bonds via backward stochastic differential equations (BSDEs). By virtue of reflected BSDEs and Malliavin derivatives, we establish the formulae for the fair price of convertible bonds and the hedging portfolio strategy explicitly. …”
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Stochastic Predator-Prey System Subject to Lévy Jumps by Xinzhu Meng, Xiaohong Wang

“…In addition, we obtain the sufficient conditions for almost sure permanence in mean and stochastic permanence of the system by using the theory of impulsive stochastic differential equations. Finally, we discuss the biological implications of the main results and show that the large noise can make the system go extinct. …”
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Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps by Guodong Liu, Xiaohong Wang, Xinzhu Meng, Shujing Gao

“…Furthermore, persistence in mean of the system is also investigated by using the theory of impulsive stochastic differential equations (ISDE) and delay differential equations (DDE). …”
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Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps by Tingting Ma, Xinzhu Meng, Zhengbo Chang

“…Using the comparison theorem of stochastic differential equations and asymptotic approaches, sufficient conditions for persistence in mean and extinction of three species are derived. …”
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