Simulating systems of Itô SDEs with split-step (α,β)-Milstein scheme by Hassan Ranjbar, Leila Torkzadeh, Dumitru Baleanu, Kazem Nouri

“…In the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. …”
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Equivalent non-Gaussian excitation method for moment calculation of non-Gaussian randomly excited systems by Takahiro TSUCHIDA, Koji KIMURA

“…Generally, moment equations for the response, which are derived from the stochastic differential equation for the excitation and the equation of motion of the system, are not closed form due to the complex nonlinearity of the diffusion coefficient in the governing equation for the excitation even though the system is linear. …”
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A fast Markovian method for modeling channel noise in neurons by Norbert Ankri, Dominique Debanne

“…Our fast MC (FMC) model does not exhibit the drawbacks due to approximations based on stochastic differential equations and the values of spike jitter are comparable to those obtained with the true Markovian method. …”
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Treatment of Mode Coupling in Step-Index Multimode Microstructured Polymer Optical Fibers by the Langevin Equation by Svetislav Savović, Linqing Li, Isidora Savović, Alexandar Djordjevich, Rui Min

“…We demonstrated that by solving the Langevin equation (stochastic differential equation), one can successfully treat a mode coupling in multimode SI mPOF as a stochastic process, since it is caused by its intrinsic random perturbations. …”
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Reduced basis techniques for stochastic problems by Boyaval, S., Le Bris, C., Lelievre, T., Maday, Yvon, Nguyen, Ngoc Cuong, Patera, Anthony T.

“…Sci., 2009, which uses a RB type approach to reduce the variance in the Monte-Carlo simulation of a stochastic differential equation. We conclude the review with some general comments and also discuss possible tracks for further research in the direction.…”
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Stochastic particle transport by deep-water irregular breaking waves by Eeltink, D, Calvert, R, Swagemakers, JE, Xiao, Q, van den Bremer, TS

“…To model particle transport in irregular waves, some of which break, we develop a stochastic differential equation describing both mean particle transport and its uncertainty. …”

Arbitrary-Order Finite-Time Corrections for the Kramers–Moyal Operator by Leonardo Rydin Gorjão, Dirk Witthaut, Klaus Lehnertz, Pedro G. Lind

“…This expansion is necessary for deriving the different terms in a stochastic differential equation. With the full representation of this operator, we are able to separate finite-time corrections of the power-series expansion of arbitrary order into terms with and without derivatives of the Kramers–Moyal coefficients. …”
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Pricing of Pseudo-Swaps Based on Pseudo-Statistics by Sebastian Franco, Anatoliy Swishchuk

“…A data/statistics-based approach to swap pricing is very different from stochastic volatility models such as the Cox–Ingresoll–Ross (CIR) model, which, in comparison, follows a stochastic differential equation. Although there are many other stochastic models that provide an approach to calculating the price of swaps, we will use the CIR model for comparison within this paper, due to the popularity of the CIR model. …”
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Unreliable communication in high-performance distributed multi-agent systems: A ingenious scheme in high computing by Ali Mustafa, Muhammad Najam ul Islam, Salman Ahmed, Muhammad Ahsan Tufail

“…The proposed algorithm paces up the rate of convergence by reducing the number of iteration, along with sure convergence of the designed algorithm using the concepts of stochastic differential equation theory, control system theory, algebraic graph theory, and algebraic matrix theory. …”
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The dynamics of novel corona virus disease via stochastic epidemiological model with vaccination by Rahman Ullah, Qasem Al Mdallal, Tahir Khan, Roman Ullah, Basem Al Alwan, Faizullah Faiz, Quanxin Zhu

“…We develop the epidemic problem by taking into account the extended version of the susceptible-infected-recovered model and with the aid of a stochastic differential equation. We then study the fundamental axioms for existence and uniqueness to show that the problem is mathematically and biologically feasible. …”
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Nonlinear diffusion and hyperuniformity from Poisson representation in systems with interaction mediated dynamics by Thibault Bertrand, Didier Chatenay, Raphaël Voituriez

“…Using Poisson representations, our model is amenable to an exact nonlinear stochastic differential equation. We derive analytically its hydrodynamic limit, which turns out to be a nonlinear diffusion equation of porous medium type valid even far from steady state. …”
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Bayesian on-line anticipation of critical transitions by Martin Heßler, Oliver Kamps

“…We present a data-driven method based on the estimation of a parameterized nonlinear stochastic differential equation that allows for a robust anticipation of critical transitions even in the presence of strong noise which is a characteristic of many real world systems. …”
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Anisotropic (2+1)d growth and Gaussian limits of q-Whittaker processes by Corwin, Ivan, Ferrari, Patrik L., Borodin, Alexei

“…By considering certain Gaussian stochastic differential equation limits of the model we are able to prove a space-time limit of covariances to those of the (2 + 1)-dimensional additive stochastic heat equation (or Edwards-Wilkinson equation) along characteristic directions. …”
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Non-asymptotic bounds for modified tamed unadjusted Langevin algorithm in non-convex setting by Ng, Matthew Cheng En

“…We consider the problem of sampling from a target distribution $\pi_\beta$ on $\mathbb{R}^d$ with density proportional to $\theta\mapsto e^{-\beta U(\theta)}$ using explicit numerical schemes based on discretising the Langevin stochastic differential equation (SDE). In recent literature, taming has been proposed and studied as a method for ensuring stability of Langevin-based numerical schemes in the case of super-linearly growing drift coefficients for the Langevin SDE. …”
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Robust time-inconsistent stochastic linear-quadratic control with drift disturbance by Han, Bingyan, Pun, Chi Seng, Wong, Hoi Ying

“…Under a general framework allowing random parameters, we derive a sufficient condition for equilibrium controls using the forward-backward stochastic differential equation approach. We also provide analytical solutions to mean-variance portfolio problems for various settings. …”
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Asymptotic expansions and distribution properties for diffusion processes by She, Qihao

“…Lastly, we consider a multidimensional ergodic Ornstein-Uhlenbeck process, X and let Y be a multidimensional stochastic process such that its stochastic differential equation is written as a drift-perturbation of X and µY be the stationary distribution of Y. …”
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The spatial Lambda-Fleming-Viot process with fluctuating selection by Biswas, N, Etheridge, AM, Klimek, A

“…We consider first a population with no spatial structure, modelled by an adaptation of the Lambda (or generalised) Fleming-Viot process, and derive a stochastic differential equation as a scaling limit. This amounts to a limit result for a LambdaFleming-Viot process in a rapidly fluctuating random environment. …”

Price modelling and asset valuation in carbon emission and electricity markets by Schwarz, D

“…The allowance price is obtained as the solution to a coupled forward-backward stochastic differential equation. We provide a rigorous proof of the existence and uniqueness of a solution to this equation and analyse its behaviour using asymptotic techniques. …”

Parameter estimation of the stochastic model for oral cancer in response to thymoquinone (TQ) as anticancer therapeutics by Tabassum, Shabana, Rosli, Norhayati, Jauhari Arief, Solachuddin

“…This article models the decelerating of the oral cancer growth by using a linear stochastic differential equation (SDEs). The Markov Chain Monte Carlo (MCMC) method used to estimate model parameters for 100, 500,1000 and 2000 simulations. …”
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Constrained stochastic differential games with Markovian switchings and additive structure: The total expected payoff by Beatris Adriana Escobedo-Trujillo, José Daniel López-Barrientos, Javier Garrido, Darío Colorado-Garrido, José Vidal Herrera-Romero

“…Therein, the evolution is governed by a linear stochastic differential equation with Markovian switching, and the decay pollution rate depends on a Markov chain.…”
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