Convergence in Distribution of Some Self-Interacting Diffusions by Aline Kurtzmann

“…These diffusions are solutions to stochastic differential equations: dXt=dBt-g(t)∇V(Xt-μ¯t)dt, where μ¯t is the empirical mean of the process X, V is an asymptotically strictly convex potential, and g is a given positive function. …”
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The Quantum Analysis of Nonlinear Optical Parametric Processes with Thermal Reservoirs by Tamirat Abebe, Nebiyu Gemechu, Chimdessa Gashu, Kebede Shogile, Solomon Hailemariam, Shimelis Adisu

“…In this paper, employing the stochastic differential equations associated with the normal ordering, the quantum properties of a nondegenerate three-level cascade laser with a parametric amplifier and coupled to a two-mode thermal reservoir are thoroughly analyzed. …”
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A Bright Entanglement and Squeezing Generated by an External Pumping Radiation in a Correlated Emission Laser by Chimdessa Gashu

“…The quantum and statistical properties of light generated by an external classical field in a correlated emission laser with a parametric amplifier and coupled to a squeezed vacuum reservoir are investigated using the combination of the master and stochastic differential equations. First, the solutions of the cavity-mode variables and correlation properties of noise forces associated to the normal ordering are obtained. …”
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Adaptive Synchronization for Two Different Stochastic Chaotic Systems with Unknown Parameters via a Sliding Mode Controller by Zengyun Wang, Lihong Huang, Xuxin Yang, Dingyang Lu

“…Firstly, based on the Lyapunov theory in stochastic differential equations and the theory of sliding mode control, we propose a simple sliding surface and discuss the occurrence of the sliding motion. …”
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Optimal Portfolio Selection of Mean-Variance Utility with Stochastic Interest Rate by Shuang Li, Shican Liu, Yanli Zhou, Yonghong Wu, Xiangyu Ge

“…In order to tackle the problem of how investors in financial markets allocate wealth to stochastic interest rate governed by a nested stochastic differential equations (SDEs), this paper employs the Nash equilibrium theory of the subgame perfect equilibrium strategy and propose an extended Hamilton-Jacobi-Bellman (HJB) equation to analyses the optimal control over the financial system involving stochastic interest rate and state-dependent risk aversion (SDRA) mean-variance utility. …”
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Analysis and Enhancements of a Prolific Macroscopic Model of Epilepsy by Christopher Fietkiewicz, Kenneth A. Loparo

“…Specifically, we analyze three aspects of the models: (1) Using dynamical systems analysis, we demonstrate and explain the presence of direct current potentials in the simulated EEG that were previously undocumented. (2) We explain how the system was not ideally formulated for numerical integration of stochastic differential equations. A reformulated system is developed to support proper methodology. (3) We explain an unreported contradiction in the published model specification regarding the use of a mathematical reduction method. …”
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Threshold dynamics of stochastic SIRSW infectious disease model with multiparameter perturbation by Zhengwen Yin, Yuanshun Tan

“…In addition to establishing the existence and uniqueness of the global positive solution of the model, we derived the threshold conditions for the extinction and persistence of the disease using the comparison theorem and It$ \hat{o} $'s formula of stochastic differential equations. Subsequently, we obtained the asymptotic stability of both the disease-free equilibrium and the endemic equilibrium of the deterministic model corresponding to the stochastic model through stochastic stability theory. …”
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The Stochastic Resonance Phenomenon of Different Noises in Underdamped Bistable System by Shan Yang, Zening Fan, Ruibin Ren

“…By applying theory of stochastic differential equations to the numerical simulation of stochastic resonance problem, we simulate and analyze the system responses and pay close attention to stochastic control in the proposed systems. …”
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Adaptive Time-Stepping Using Control Theory for the Chemical Langevin Equation by Silvana Ilie, Monjur Morshed

“…This model is represented as a system of stochastic differential equations, with multiplicative and noncommutative noise. …”
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Dynamics of the Exponential Population Growth System with Mixed Fractional Brownian Motion by Weijun Ma, Wei Liu, Quanxin Zhu, Kaibo Shi

“…First, we establish some useful lemmas that provide powerful tools for studying the stochastic differential equations with mixed fractional Brownian motion. …”
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Backward Anticipated Social Optima: Input Constraints and Partial Information by Shujun Wang

“…Furthermore, differently from the classic social optima literature, the dynamics in this framework are driven by <i>anticipated</i> backward stochastic differential equations (ABSDE) in which the <i>terminal</i> instead of the <i>initial</i> condition is specified and the anticipated terms are involved. …”
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Stochastic control with state constraints via the Fokker–Planck equation. Application to renewable energy plants with batteries by Bermúdez, Alfredo, Padín, Iago

“…Firstly, a stochastic model of a wind power plant with battery storage is stated in the framework of stochastic differential equations (SDE). Then, a stochastic control problem with state constraints is introduced and the corresponding optimality conditions involving the Hamilton–Jacobi–Bellman equation are deduced. …”
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Application of BSDE in Standard Inventory Financing Loan by Hui Zhang, Wenyu Meng, Xiaojie Wang, Jianwei Zhang

“…Applying backward stochastic differential equations (BSDEs), we get the explicit solutions of the models. …”
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The levelized cost of energy in the presence of uncertainty on the offshore wind speed by J. Pablo Arenas-López, Mohamed Badaoui

“…To carry out this task, we employ two techniques based on stochastic differential equations to generate wind power scenarios. …”
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Stratifications and foliations in phase portraits of gene network models by V. P. Golubyatnikov, A. A. Akinshin, N. B. Ayupova, L. S. Minushkina

“…Description of the phase portraits of these systems at the level of their stratifications, and that of ensembles of trajectories allows one to construct more realistic gene network models on the basis of methods of statistical physics and the theory of stochastic differential equations.…”
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