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Representations and classifications of stochastic processes [PDF]
Transactions of the American Mathematical Society, 1974 We show that to every stochastic process X one can associate a unique collection ( Φ
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Laplacian Autoencoders for Learning Stochastic Representations [PDF]
Advances in Neural Information Processing Systems 35, 2022 Established methods for unsupervised representation learning such as variational autoencoders produce none or poorly calibrated uncertainty estimates making it difficult to evaluate if learned representations are stable and reliable. In this work, we present a Bayesian autoencoder for unsupervised representation learning, which is trained using a novel
Miani, Marco +4 more
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Electronic Journal of Qualitative Theory of Differential Equations, 2004 The main object of this paper is to give a representation of the covariance operator associated to the mild solutions of time-varying,linear, stochastic equations in Hilbert spaces.
V. M. Ungureanu
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Complexity, 2023 In this article, we consider the Nash equilibrium of stochastic differential game where the state process is governed by a controlled stochastic partial differential equation and the information available to the controllers is possibly less than the ...
Gaofeng Zong
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A Study of The Stochastic Burgers’ Equation Using The Dynamical Orthogonal Method
Axioms, 2023 In the current work, the stochastic Burgers’ equation is studied using the Dynamically Orthogonal (DO) method. The DO presents a low-dimensional representation for the stochastic fields. Unlike many other methods, it has a time-dependent property on both
Mohamed El-Beltagy +2 more
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A stochastic model for natural feature representation [PDF]
, 2005 This paper presents a robust stochastic model for the incorporation of natural features within data fusion algorithms. The representation combines Isomap, a non-linear manifold learning algorithm, with Expectation Maximization, a statistical learning ...
Sakkarieh, S. +13 more
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Aumann Type Set-valued Lebesgue Integral and Representation Theorem [PDF]
International Journal of Computational Intelligence Systems, 2009 n this paper, we shall firstly illustrate why we should discuss the Aumann type set-valued Lebesgue integral of a set-valued stochastic process with respect to time t under the condition that the set-valued stochastic process takes nonempty compact ...
Jungang Li, Shoumei Li
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A class of stochastic Gronwall’s inequality and its application
Journal of Inequalities and Applications, 2018 This paper puts forward the basic form of stochastic Gronwall’s inequality and uses, respectively, the iterative method, the integral method and the martingale representation method to prove it.
Xin Wang, Shengjun Fan
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Modelling the operation of multireservoir systems using decomposition and stochastic dynamic programming [PDF]
, 2006 Stochastic dynamic programming models are attractive for multireservoir control problems because they allow non-linear features to be incorporated and changes in hydrological conditions to be modeled as Markov processes.
Archibald, Thomas W.; id_orcid +5 more
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A stochastic representation of the local structure of turbulence [PDF]
EPL (Europhysics Letters), 2010 Based on the mechanics of the Euler equation at short time, we show that a Recent Fluid Deformation (RFD) closure for the vorticity field, neglecting the early stage of advection of fluid particles, allows to build a 3D incompressible velocity field that shares many properties with empirical turbulence, such as the teardrop shape of the R-Q plane ...
Chevillard, Laurent +2 more
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