A boundary preserving numerical algorithm for the Wright-Fisher model with mutation by Dangerfield, C, Kay, D, MacNamara, S, Burrage, K

“…The Wright-Fisher model is an Itô stochastic differential equation that was originally introduced to model genetic drift within finite populations and has recently been used as an approximation to ion channel dynamics within cardiac and neuronal cells. …”

Risk-Neutral Pricing of Financial Instruments in Emission Markets: A Structural Approach by Howison, S, Schwarz, D

“…We derive a forward-backward stochastic differential equation for the price process of the allowance certificate and solve the associated semilinear partial differential equation numerically. …”

Global-in-time solutions and qualitative properties for the NNLIF neuron model with synaptic delay by Caceres, MJ, Roux, PJA, Salort, D, Schneider, R

“…The Nonlinear Noisy Leaky Integrate and Fire (NNLIF) model is widely used to describe the dynamics of neural networks after a diffusive approximation of the mean-field limit of a stochastic differential equation system. When the total activity of the network has an instantaneous effect on the network, in the average-excitatory case, a blow-up phenomenon occurs. …”

Pricing Sukuk of Mushurakah Ventures Using its Expected Return; (A case study of Iran OTC) by Rafie Hasani Moghaddam

“…In this paper, the Mushurakah bonds (Sukuk) pricing model using expected return in the form of a stochastic differential equation is presented and this stochastic differential model is transformed into a partial differential equation using the self-financing basket and then solved by numerical finite difference method. …”
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Stochastic Thermodynamics of an Electromagnetic Energy Harvester by Luigi Costanzo, Alessandro Lo Schiavo, Alessandro Sarracino, Massimo Vitelli

“…We describe the system with a linear model, featuring an underdamped stochastic differential equation for an effective mass in a harmonic potential, coupled electromechanically with the current in the circuit. …”
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A Numerical solution for the new model of time-fractional bond pricing‎: ‎Using a multiquadric approximation method by Sedighe sharifian, Ali Soheili, Abdolsadeh Neisy

“…In terms of maturities ‎, ‎bonds are divided into three categories as follows‎ : ‎short term‎ , ‎medium term‎ , ‎and long ‎term‎ .‎‎In this paper‎ , ‎we model the fractional bond pricing under fractional stochastic differential equation ‎. ‎We implement the multiquadric approximation for solving the fractional bond pricing equation‎ . ‎…”
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A γ-power stochastic Lundqvist-Korf diffusion process: Computational aspects and simulation by Abdenbi El Azri, Ahmed Nafidi

“…First, we determine the probabilistic characteristics of the process, such as its analytic expression, the transition probability density function from the corresponding It ˆo stochastic differential equation and obtain the conditional and non-conditional mean functions. …”
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Unconditionally stable monte carlo simulation for solving the multi-dimensional Allen–Cahn equation by Youngjin Hwang, Ildoo Kim, Soobin Kwak, Seokjun Ham, Sangkwon Kim, Junseok Kim

“…The diffusion term is calculated using MCS for the stochastic differential equation, while the nonlinear term is locally computed for each particle in a virtual grid. …”
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Anticipated BSDEs Driven by Fractional Brownian Motion with a Time-Delayed Generator by Pei Zhang, Adriana Irawati Nur Ibrahim, Nur Anisah Mohamed

“…This article describes a new form of an anticipated backward stochastic differential equation (BSDE) with a time-delayed generator driven by fractional Brownian motion, further known as fractional BSDE, with a Hurst parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>. …”
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Optimal Exploitation of a General Renewable Natural Resource under State and Delay Constraints by M’hamed Gaïgi, Idris Kharroubi, Thomas Lim

“…The resource is assumed to evolve according to a logistic stochastic differential equation. The manager is allowed to harvest the resource and sell it at a stochastic market price modeled by a geometric Brownian process. …”
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Simple Closed-Form Formulas for Conditional Moments of Inhomogeneous Nonlinear Drift Constant Elasticity of Variance Process by Kittisak Chumpong, Raywat Tanadkithirun, Chanon Tantiwattanapaibul

“…The stochastic differential equation (SDE) has been used to model various phenomena and investigate their properties. …”
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Nonlinear optimization algorithm using monotonically increasing quantization resolution by Jinwuk Seok, Jeong-Si Kim

“…Thus, we rewrite the searching equation based on a gradient descent as a stochastic differential equation and obtain the monotonically decreasing rate of the quantization step, enabling the global optimization by stochastic analysis for deriving an objective function. …”
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Optimal Incentive Contract for Sales Team with Loss Aversion Preference by Chao Li, Si-Jie Cheng, Peng-Fei Cheng

“…We use a backward stochastic differential equation (BSDE) to represent agents&#8217; contract through the martingale representation theorem and use the stochastic optimal control and matrix method to obtain the explicit solution of the optimal contract. …”
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Exact analysis of the response of quantum systems to two-photons using a QSDE approach by Yu Pan, Daoyi Dong, Guofeng Zhang

“…We introduce the quantum stochastic differential equation (QSDE) approach to exactly analyze the response of quantum systems to a continuous-mode two-photon input. …”
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Correlated stochastic epidemic model for the dynamics of SARS-CoV-2 with vaccination by Tahir Khan, Roman Ullah, Basem Al Alwan, Youssef El-Khatib, Gul Zaman

“…As the environmental reservoir plays a weighty role in the transmission of the SARS-CoV-2 virus, our model encompasses a fourth stochastic differential equation representing the reservoir. Moreover, the vaccination of susceptible is also considered. …”
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Fast stochastic simulation of biochemical reaction systems by alternative formulations of the Chemical Langevin Equation by Mélykúti, B, Burrage, K, Zygalakis, K

“…The Chemical Langevin Equation (CLE), which is a stochastic differential equation (SDE) driven by a multidimensional Wiener process, acts as a bridge between the discrete Stochastic Simulation Algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. …”

Stochastic control for linear systems driven by fractional noises by Yaozhong, H, Zhou, X

“…First, as a prerequisite for studying the underlying control problems, some new results on stochastic integrals and stochastic differential equations associated with FBM are established. …”

Application of stochastic phenomenological modelling to cell-to-cell and beat-to-beat electrophysiological variability in cardiac tissue by Walmsley, J, Mirams, GR, Pitt-Francis, J, Rodriguez, B, Burrage, K

“…We developed four cell-specific parameterizations of a phenomenological stochastic differential equation AP model exhibiting intrinsic variability using APs recorded from isolated guinea pig ventricular myocytes exhibiting BVR. …”

Stochastic Models and Simulation of Ion Channel Dynamics by Dangerfield, C, Kay, D, Burrage, K, ICCS

“…By assuming that such transition rates are constant over each time step, it is possible to derive a stochastic differential equation (SDE), in the same manner as for biochemical reaction networks, that describes the stochastic dynamics of ion channels. …”

A numerical scheme for the quantile hedging problem by Bénézet, C, Chassagneux, J-F, Reisinger, C

“…We prove convergence in the monotone case combining backward stochastic differential equation arguments with the Barles and Jakobsen and Barles and Souganidis approaches for nonlinear PDEs. …”