A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise by Wang, Xiaojie, Gan, Siqing, Wang, Desheng

“…In this paper a family of fully implicit Milstein methods are introduced for solving stiff stochastic differential equations (SDEs). It is proved that the methods are convergent with strong order 1.0 for a class of SDEs. …”
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Characterization of stochastic equilibrium controls by the Malliavin calculus by Nguwi, Jiang Yu, Privault, Nicolas

Subjects: “…Backward Stochastic Differential Equation…”
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Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees by Nguwi, Jiang Yu, Privault, Nicolas

“…Our implementation uses neural networks that yield a functional space-time domain estimation, and includes numerical comparisons with the deep Galerkin (DGM) and deep backward stochastic differential equation (BSDE) methods.…”
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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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Parabolic systems and stochastic controls: nonlocality, nonlinearity, and time-inconsistency by Lei, Qian

“…This thesis aims to advance the theories of partial differential equation (PDE) and stochastic differential equation (SDE), and by which, we address decade-long open problems in the field of stochastic controls. …”
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Optimal control and stabilization for Itô systems with input delay by Wang, Hongxia, Zhang, Huanshui, Xie, Lihua

“…The authors provide a way to solve the delayed forward backward stochastic differential equation (D-FBSDE) arising from the maximum principle. …”
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A deep branching solver for fully nonlinear partial differential equations by Nguwi, Jiang Yu, Penent, Guillaume, Privault, Nicolas

“…Numerical experiments presented show that this algorithm can outperform deep learning approaches based on backward stochastic differential equations or the Galerkin method, and provide solution estimates that are not obtained by those methods in fully nonlinear examples.…”
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Stochastic orderings by nonlinear expectations by Ly, Sel

“…Our approach relies on comparison lemmas for forward-backward, and for G-forward-backward stochastic differential equations, and on several extensions of monotonicity, convexity and continuous dependence property for the solutions of associated semilinear parabolic partial differential equations and Hamilton-Jacobi-Bellman-type equations. …”
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Quantum synchronization: insights and applications to quantum information processing by Shen, Yuan

“…Building on a robust theoretical framework encompassing appropriate quantum master equations, quantum stochastic differential equations, and quantum trajectory techniques, this research uncovers genuine quantum phenomena in synchronization, particularly in highly nonlinear quantum oscillators. …”
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Inferring temporal dynamics from cross-sectional data using Langevin dynamics by Dutta, Pritha, Quax, Rick, Crielaard, Loes, Badiali, Luca, Sloot, Peter M. A.

“…The result is a set of stochastic differential equations that capture the temporal dynamics, by assuming that groups of data-points are subject to the same free energy landscape and amount of noise. …”
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Nonlocal fully nonlinear parabolic differential equations arising in time-inconsistent problems by Lei, Qian, Pun, Chi Seng

“…Moreover, we reveal that the solution of a nonlocal fully nonlinear parabolic PDE is an adapted solution to a flow of second-order forward-backward stochastic differential equations.…”
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Deep learning-based numerical methods for partial differential equations by Dou, Yao

“…The objective of this Final Year Project is to study deep learning-based numerical methods, with a focus on the Deep BSDE Solver, that can be applied on stochastic control problems, backward stochastic differential equations (BSDE) and partial differential equations (PDE) in high-dimensional space. …”
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Improving representation learning on graph-structural data for classification, generation, and recommendation by Luo, Tianze

“…GSDM utilizes low-rank diffusion Stochastic Differential Equations in graph spectrum space, enhancing graph topology generation and reducing computational load. …”
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Sequence-to-sequence learning for motion prediction and generation by Wu, Shuang

“…Finally, we reconsider motion prediction within the framework of stochastic differential equations, which allows for interpretation of model weights as the stochastic diffusion matrix and drift parameters. …”
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Computational modelling of the biological and social factors of type 2 diabetes by Dutta, Pritha

“…The result is a set of stochastic differential equations which capture the temporal dynamics, by assuming that groups of data-points are subject to the same free energy landscape and amount of noise. …”
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