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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Malliavin calculus in a binomial framework by Cohen, S, Elliott, R, Siu, T

“…Martingale representation, backward stochastic differential equations, and the Malliavin calculus are difficult concepts in a continuous‐time setting. …”

Haar Wavelet Method for Series Expansion of Fractional Wiener Integral

“…Thus, finding an accurate and efficient numerical method for solving stochastic differential equations, and stochastic integral equations is important. …”
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Improved multilevel Monte Carlo convergence using the Milstein scheme by Giles, M

“…In this paper we show that the Milstein scheme can be used to improve the convergence of the multilevel Monte Carlo method for scalar stochastic differential equations, so that the computational cost to achieve a root-mean-square error of $\epsilon$ is reduced to $O(\epsilon^{-2})$. …”

A Novel Averaging Principle Provides Insights in the Impact of Intratumoral Heterogeneity on Tumor Progression by Haralampos Hatzikirou, Nikos I. Kavallaris, Marta Leocata

“…Typically stochastic differential equations (SDEs) involve an additive or multiplicative noise term. …”
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Performance of Eular-Maruyama, 2-stage SRK and 4-stage SRK in approximating the strong solution of stochastic model by Norhayati Rosli, Arifah Bahar, Yeak, Su Hoe, Haliza Abdul Rahman, Madihah Md. Salleh

“…Stochastic differential equations play a prominent role in many application areas including finance, biology and epidemiology. …”
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Performance of Euler-Maruyama, 2-Stage SRK and 4-Stage SRK in approximating the strong solution of stochastic model by Rosli, Norhayati, Bahar, Arifah, Su Hoe, Yeak, Abdul Rahman, Haliza, Md. Salleh, Madihah

“…Stochastic differential equations play a prominent role in many application areas including finance, biology and epidemiology. …”

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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New Simplified High-Order Schemes for Solving SDEs with Markovian Switching Driven by Pure Jumps by Yang Li, Yingmei Xu, Qianhai Xu, Yu Zhang

“…New high-order weak schemes are proposed and simplified to solve stochastic differential equations with Markovian switching driven by pure jumps (PJ-SDEwMs). …”
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The S-asymptotically ω-periodic solutions for stochastic fractional differential equations with piecewise constant arguments by Shufen Zhao

“…In this paper, two kinds of stochastic differential equations with piecewise constant arguments are investigated. …”
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Generalized BSDEs driven by RCLL martingales with stochastic monotone coefficients by Badr Elmansouri, Mohamed El Otmani

“…A solution is given to generalized backward stochastic differential equations driven by a real-valued RCLL martingale on an arbitrary filtered probability space. …”
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Computational Principle and Performance Evaluation of Coherent Ising Machine Based on Degenerate Optical Parametric Oscillator Network by Yoshitaka Haribara, Shoko Utsunomiya, Yoshihisa Yamamoto

“…A quantum theory of CIM is formulated, and the computational ability of CIM is evaluated by numerical simulation based on c-number stochastic differential equations. We also discuss the advanced CIM with quantum measurement-feedback control and various problems which can be solved by CIM.…”
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Likelihood inference for Discretely Observed Non-linear Diffusions. by Elerian, O, Chib, S, Shephard, N

“…This paper is concerned with the Bayesian estimation of non-linear stochastic differential equations when only discrete observations are available. …”

Integrability and tail estimates for Gaussian rough differential equations by Cass, T, Litterer, C, Lyons, T

“…We derive explicit tail-estimates for the Jacobian of the solution flow for stochastic differential equations driven by Gaussian rough paths. …”

Continuous time dynamics of the thermal minority game by Garrahan, J, Moro, E, Sherrington, D

“…We find that the dynamical equations of the model reduce to a set of stochastic differential equations for an interacting disordered system with nontrivial random diffusion. …”

Reflected generalized discontinuous BSDEs with rcll barrier and an obstacle problem of IPDE with nonlinear Neumann boundary conditions by Mohammed Elhachemy, Mohamed El Otmani

“…Reflected generalized backward stochastic differential equations (BSDEs) with one discontinuous barrier are investigated when the noise is driven by a Brownian motion and an independent Poisson measure. …”
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Provincial Oil Budget Allocation based on a Stochastic Optimal Control Model by Hadi Rahmani Fazli, Abbas Arabmazar

“…Accordingly, different models of stochastic differential equations and stochastic optimal control for modeling oil price and petroleum budgets allocation in different years are proposed. …”
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A functional approach to backward stochastic dynamics by Liang, G

“…<p>In this thesis, we consider a class of stochastic dynamics running backwards, so called backward stochastic differential equations (BSDEs) in the literature. We demonstrate BSDEs can be reformulated as functional differential equations defined on path spaces, and therefore solving BSDEs is equivalent to solving the associated functional differential equations. …”

Multiscale systems, homogenization, and rough paths by Chevyrev, I, Friz, P, Korepanov, A, Melbourne, I, Zhang, H

“…In recent years, substantial progress was made towards understanding convergence of fast-slow deterministic systems to stochastic differential equations. In contrast to more classical approaches, the assumptions on the fast flow are very mild. …”

Multivalued Impulsive SDEs Driven by G-Brownian Noise: Periodic Averaging Result by Mahmoud Abouagwa, Anas D. Khalaf, Nadia Gul, Sultan Alyobi, Al-Sharef Mohamed

“…This paper aims to study two approximation theorems in view of the periodic averaging results for non-Lipschitz multivalued stochastic differential equations with impulses and G-Brownian motion (MISDEGs). …”
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