Dynamics of single-domain magnetic particles at elevated temperatures by M Tzoufras, M K Grobis

“…A stochastic differential equation that describes the dynamics of single-domain magnetic particles at any temperature is derived using a classical formalism. …”
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Bautin bifurcation with additive noise by Tang Diandian, Ren Jingli

“…In this paper, we consider stochastic dynamics of a two-dimensional stochastic differential equation with additive noise. When the strength of the noise is zero, this equation undergoes a Bautin bifurcation. …”
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Numerical Solution of an Interval-Based Uncertain SIR (Susceptible–Infected–Recovered) Epidemic Model by Homotopy Analysis Method by Emmanuel A. Bakare, Snehashish Chakraverty, Radovan Potucek

“…Furthermore, the SIR ODE model was transformed into a stochastic differential equation (SDE) model and the results of the stochastic and deterministic models were compared using numerical simulations. …”
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Approximating Correlation Matrices Using Stochastic Lie Group Methods by Michelle Muniz, Matthias Ehrhardt, Michael Günther

“…Based on isospectral flows we create valid time-dependent correlation matrices, so called correlation flows, by solving a stochastic differential equation (SDE) that evolves in the special orthogonal group. …”
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A study of stochastic epidemic model driven by liouville fractional brownian motion coupled with seasonal air pollution by Suryawan Herry Pribawanto

“…Since there are many uncertain factors in the environment, stochastic differential equation model is a powerful tool to study the changes of air pollution and the transmission of infectious diseases. …”
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On the uniqueness of solutions to quadratic BSDEs with non-convex generators and unbounded terminal conditions by Fan, Shengjun, Hu, Ying, Tang, Shanjian

“…We prove a uniqueness result of the unbounded solution for a quadratic backward stochastic differential equation whose terminal condition is unbounded and whose generator $g$ may be non-Lipschitz continuous in the state variable $y$ and non-convex (non-concave) in the state variable $z$, and instead satisfies a strictly quadratic condition and an additional assumption. …”
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STOCHASTIC BIFURCATION OF A CURRENT CARRYING THIN RECTANGULAR PLATE IN A MAGNETIC FIELD by WANG Ping, WEI Xing, WANG ZhiRen

“…Then the equation was equivalent to be a one-dimensional It stochastic differential equation by applying the stochastic average theory of a quasi non-integrable Hamilton system. …”
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Rough path limits of the Wong–Zakai type with a modified drift term by Friz, P, Oberhauser, H

“…The Wong-Zakai theorem asserts that ODEs driven by "reasonable" (e.g. piecewise linear) approximations of Brownian motion converge to the corresponding Stratonovich stochastic differential equation. With the aid of rough path analysis, we study "non-reasonable" approximations and go beyond a well-known criterion of [Ikeda, Watanabe, North Holland, 1989] in the sense that our result applies to perturbations on all levels, exhibiting additional drift terms involving any iterated Lie brackets of the driving vector fields. …”

Integral representation of martingales motivated by the problem of endogenous completeness in financial economics by Kramkov, D, Predoiu, S

“…Let Q and P be equivalent probability measures and let ψ be a J-dimensional vector of random variables such that dQ/dP and ψ are defined in terms of a weak solution X to a d-dimensional stochastic differential equation. Motivated by the problem of endogenous completeness in financial economics we present conditions which guarantee that every local martingale under Q is a stochastic integral with respect to the J-dimensional martingale Stδ EQ[ψ|Ft]. …”

COMPENSATION OF THE DOPPLER SHIFT OF THE RADIO ALTIMETER ON A HIGH-SPEED CARRIER by M.Yu. Nesterov

“…Obtained filtering algorithm was verified with altimeter simulation model included stochastic differential equation of the dynamic tracking loop. …”

Optimal control analysis of deterministic and stochastic epidemic model with media awareness programs by Shrishail Ramappa Gani, Shreedevi Veerabhadrappa Halawar

“…The present study considered the optimal control analysis of  both deterministic differential equation modeling and stochastic differential equation modeling of infectious disease by taking effects of media awareness programs  and treatment of infectives on the epidemic into account. …”
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Deterministic and Stochastic Prey–Predator Model for Three Predators and a Single Prey by Yousef Alnafisah, Moustafa El-Shahed

“…The exponential–mean–squared stability of the resulting stochastic differential equation model was examined, and it was found to be dependent on the harvesting effort. …”
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Pricing of vulnerable options based on an uncertain CIR interest rate model by Guiwen Lv, Ping Xu, Yanxue Zhang

“…The traditional Cox-Ingersoll-Ross (CIR) interest rate model follows a stochastic differential equation that cannot obtain the closed solution while the uncertain CIR interest rate model is an uncertain differential equation. …”
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Sensitivity Analysis of Optimal Commodity Decision Making with Neural Networks: A Case for COVID-19 by Nader Karimi, Erfan Salavati, Hirbod Assa, Hojatollah Adibi

“…The method uses an artificial neural network (ANN) to approximate the optimal value function for a general stochastic differential equation and calculate the partial derivatives of the value function with respect to various parameters of both the diffusion process and the payoff function. …”
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Pseudo-spectral optimal control of stochastic processes using Fokker Planck equation by Ali Namadchian, Mehdi Ramezani

“…Motivated by the successful implementation of Pseudo-spectral (PS) methods in optimal control problems (OCP), a new technique is introduced to control the probability density function (PDF) of the state of the 1-D system described by a stochastic differential equation (SDE). In this paper, the Fokker Planck equation (FPE) is used to model the time evolution of the PDF of the stochastic process. …”
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Research on Enterprise Investment Decision Based on Linear Quadratic Jump Uncertainty Stochastic Differential Game by Lu Yang, Chengke Zhang, Tao Wang, Xin Chen

“…The system is described by both a jump uncertain differential equation and a stochastic differential equation. The principle of optimality and equation of optimality are established. …”
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SHORT TIME FULL ASYMPTOTIC EXPANSION OF HYPOELLIPTIC HEAT KERNEL AT THE CUT LOCUS by YUZURU INAHAMA, SETSUO TANIGUCHI

“…Our approach is probabilistic and the heat kernel is regarded as the density of the law of a hypoelliptic diffusion process, which is realized as a unique solution of the corresponding stochastic differential equation. Our main tools are S. Watanabe’s distributional Malliavin calculus and T. …”
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Backward Deep BSDE Methods and Applications to Nonlinear Problems by Yajie Yu, Narayan Ganesan, Bernhard Hientzsch

“…We present a pathwise deep Backward Stochastic Differential Equation (BSDE) method for Forward Backward Stochastic Differential Equations with terminal conditions that time-steps the BSDE backwards and apply it to the differential rates problem as a prototypical nonlinear problem of independent financial interest. …”
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Calibrating FBSDEs Driven Models in Finance via NNs by Luca Di Persio, Emanuele Lavagnoli, Marco Patacca

“…In particular, we consider solving the Black–Scholes–Barenblatt non-linear stochastic differential equation via a forward-backward neural network, also calibrating the related stochastic volatility model when dealing with European options. …”
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Optimal mean-variance reinsurance and investment strategy with constraints in a non-Markovian regime-switching model by Liming Zhang, Rongming Wang, Jiaqin Wei

“…With the help of a backward stochastic differential equation driven by the Markov chain, we obtain the optimal strategy and optimal cost explicitly under this non-Markovian regime-switching model. …”
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