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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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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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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