Martingale Decomposition and Backward Stochastic Dynamic Equations on Time Scales by Guofeng Tang, Guangyan Jia

“…This work can be considered as a unification and a generalization of similar results in backward stochastic difference equations and backward stochastic differential equations.…”
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Delayed Stochastic Linear-Quadratic Control Problem and Related Applications by Li Chen, Zhen Wu, Zhiyong Yu

“…This problem will lead to a kind of generalized forward-backward stochastic differential equations (FBSDEs) with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. …”
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Trajectory Controllability of Fractional Neutral Stochastic Dynamical Systems of Order α∈1,2 With Deviating Argument by Dhanalakshmi Kasinathan, Ravikumar Kasinathan, Ramkumar Kasinathan, Karthikeyan Shanmugasundaram, Dimplekumar Chalishajar

“…In this manuscript, we establish existence, uniqueness, and trajectory controllability for higher order noninstantaneous impulsive fractional neutral stochastic differential equations. First, solvability and uniqueness results are obtained using a fixed-point approach with appropriate assumptions on nonlinear functions. …”
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Existence and Uniqueness of Solution of Stochastic Dynamic Systems with Markov Switching and Concentration Points by Taras Lukashiv, Igor Malyk

“…In this article the problem of existence and uniqueness of solutions of stochastic differential equations with jumps and concentration points are solved. …”
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Probability distribution function of the upper equatorial Pacific current speeds by Peter C. Chu

“…This is due to the different stochastic differential equations between upper and lower layers in the tropical Pacific. …”
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Dynamics of a continued fraction of Ramanujan with random coefficients by Jonathan M. Borwein, D. Russell Luke

“…We determine the convergence properties of stochastic difference equations and so the divergence of their corresponding continued fractions.…”
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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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Information predictability of stochastic processes in continuous time by A. V. Ausiannikau

“…The examples of the definition of information predictability for processes described by stochastic differential equations, are shown.…”
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Comparison Theorems for the Multidimensional BDSDEs and Applications by Bo Zhu, Baoyan Han

“…A class of backward doubly stochastic differential equations (BDSDEs) are studied. We obtain a comparison theorem of these multidimensional BDSDEs. …”
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Dynamical Behavior of the Stochastic Delay Mutualism System by Peiyan Xia, Daqing Jiang, Xiaoyue Li

“…We develop the technique for stochastic differential equations to deal with the asymptotic property. …”
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Asymptotic Behavior of Positive Solutions of a Competitive System Subject to Environmental Noise by Huili Xiang, Zhuang Fang, Zuxiong Li, Zhijun Liu

“…By using the theory of stochastic differential equations and Lyapunov function, sufficient conditions for the existence, uniqueness, stochastic boundedness, and global attraction of the positive solution of the above system are established, respectively. …”
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Formation and modeling of stochastic trajectories of multidimensional dynamic systems with assigned properties by A. V. Ausiannikau, V. M. Kozel

“…Projections phase variables on the coordinate axis of the n-dimensional hyperspace representing systems of stochastic differential equations. The proposed method allows to solve optimization problems binding parameters of stochastic trajectory with its average length and time of its passage.…”
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Dynamics of a Nonautonomous Stochastic SIS Epidemic Model with Double Epidemic Hypothesis by Haokun Qi, Lidan Liu, Xinzhu Meng

“…Moreover, the sufficient conditions for extinction of the disease are obtained by using the theory of nonautonomous stochastic differential equations. Finally, numerical simulations are utilized to illustrate our theoretical analysis.…”
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Enhancing Steady-State Entanglement Generated by a Nondegenerate Three-Level Laser with Thermal Reservoir by Tamirat Abebe, Tewodros Yirgashewa, Abebe Belay

“…We analyze a nondegenerate three-level cascade laser with an open cavity and coupled to a two-mode thermal reservoir employing the stochastic differential equations for atomic operators associated with the normal ordering. …”
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Pontryagin’s Maximum Principle for Optimal Control of Stochastic SEIR Models by Ruimin Xu, Rongwei Guo

“…The most distinguishing feature, compared with the well-studied SEIR model, is that the model system follows stochastic differential equations (SDEs) driven by Brownian motions. …”
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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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Loss formulations for assumption-free neural inference of SDE coefficient functions by Marc Vaisband, Valentin von Bornhaupt, Nina Schmid, Izdar Abulizi, Jan Hasenauer

“…Abstract Stochastic differential equations (SDEs) are one of the most commonly studied probabilistic dynamical systems, and widely used to model complex biological processes. …”
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APPROXIMATE FILTER FOR JUMP-DIFFUSION MODELS by K. A. Rybakov

“…It is assumed that the observation object and measurement system are described by Itô stochastic differential equations, the observation object equation has compound Poisson component, which allows simulating impulse noises and perturbations for control system. …”
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Discussion on exact null boundary controllability of nonlinear fractional stochastic evolution equations in Hilbert spaces by Noorah Mshary, Hamdy M. Ahmed

“…This research investigates the sufficient conditions for the null boundary controllability of Atangana-Baleanu (A-B) fractional stochastic differential equations involving fractional Brownian motion (fBm) within Hilbert space. …”
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The Optimal Control Problem with State Constraints for Fully Coupled Forward-Backward Stochastic Systems with Jumps by Qingmeng Wei

“…We focus on the fully coupled forward-backward stochastic differential equations with jumps and investigate the associated stochastic optimal control problem (with the nonconvex control and the convex state constraint) along with stochastic maximum principle. …”
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