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Négyesi, B. (author), Andersson, Kristoffer (author), Oosterlee, Cornelis W. (author)A novel discretization is presented for decoupled forward–backward stochastic differential equations (FBSDE) with differentiable coefficients, simultaneously solving the BSDE and its Malliavin sensitivity problem. The control process is estimated by the corresponding linear BSDE driving the trajectories of the Malliavin derivatives of the...journal article 2024
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Successive approximations and interval halving for fractional BVPs with integral boundary conditionsMarynets, K. (author), Pantova, D.H. (author)We study a system of non-linear fractional differential equations, subject to integral boundary conditions. We use a parametrization technique and a dichotomy-type approach to reduce the original problem to two “model-type” fractional boundary value problems with linear two-point boundary conditions. A numerical-analytic technique is applied...journal article 2024
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Binatari, N. (author), van Horssen, W.T. (author), Verstraten, P. (author), Adi-Kusumo, F. (author), Aryati, L. (author)In this paper, we present a new approach on how the multiple time-scales perturbation method can be applied to differential-delay equations such that approximations of the solutions can be obtained which are accurate on long time-scales. It will be shown how approximations can be constructed which branch off from solutions of differential...journal article 2024
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Agresti, A. (author), Veraar, M.C. (author)In this paper we introduce the critical variational setting for parabolic stochastic evolution equations of quasi- or semi-linear type. Our results improve many of the abstract results in the classical variational setting. In particular, we are able to replace the usual weak or local monotonicity condition by a more flexible local Lipschitz...journal article 2024
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Blom, H.A.P. (author)Abstract.: The transition kernel of an ℝ<sup>n</sup>-valued diffusion or jump diffusion process {X<sub>t</sub>} is known to satisfy the Feller property if {X<sub>t</sub>} is the solution of an SDE whose coefficients are Lipschitz continuous. This Lipschitz route to Feller falls short if {X<sub>t</sub>} is the solution of an SDE whose...journal article 2024
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Takali, Farid (author), Nirwal, Sonal (author), Othmani, Cherif (author), Groves, R.M. (author)It has been shown that the roots of guided waves in laminate plates produced by the ordinary differential equations (ODE) approach may not hold under to some computational conditions. A particular drawback of the 2D formulation of the ODE approach is the lack of reliability in the case of unidirectional laminates due to the decoupling...journal article 2023
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Thorpe, Matthew (author), van Gennip, Y. (author)Neural networks have been very successful in many applications; we often, however, lack a theoretical understanding of what the neural networks are actually learning. This problem emerges when trying to generalise to new data sets. The contribution of this paper is to show that, for the residual neural network model, the deep layer limit...journal article 2023
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Agresti, A. (author), Veraar, M.C. (author)In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise, critical spaces and the proof of higher order regularity of solutions – even in case of non-smooth...journal article 2023
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Liu, S. (author), Grzelak, L.A. (author), Oosterlee, C.W. (author)We propose an accurate data-driven numerical scheme to solve stochastic differential equations (SDEs), by taking large time steps. The SDE discretization is built up by means of the polynomial chaos expansion method, on the basis of accurately determined stochastic collocation (SC) points. By employing an artificial neural network to learn these...journal article 2022
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Marynets, K. (author), Pantova, D.H. (author)We use a numerical-analytic technique to construct a sequence of successive approximations to the solution of a system of fractional differential equations, subject to Dirichlet boundary conditions. We prove the uniform convergence of the sequence of approximations to a limit function, which is the unique solution to the boundary value...journal article 2022
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van Rhijn, J. (author), Oosterlee, C.W. (author), Grzelak, L.A. (author), Liu, S. (author)Generative adversarial networks (GANs) have shown promising results when applied on partial differential equations and financial time series generation. We investigate if GANs can also be used to approximate one-dimensional Ito ^ stochastic differential equations (SDEs). We propose a scheme that approximates the path-wise conditional...journal article 2022
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Oliveira de Almeida, S. (author), Chapiro, Grigori (author), Zitha, P.L.J. (author)Electromagnetic (EM) heating is an emerging method for storing renewable energy, such as photovoltaic solar and wind electric power, into aquifers. We investigate how the captured energy increases the temperature of a prototypical deep aquifer for a six-month period and then to which extent the stored energy can be recovered during the...journal article 2022
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Marynets, Vasyl (author), Marynets, K. (author), Kohutych, Oksana (author)We study a boundary value problem for a system of the third order semi-linear partial differential equations with nonlocal boundary conditions. We establish sufficient conditions of existence, uniqueness, regularity and sign-preserving property of solutions of the studied problem and construct an iterative method for its approximation.journal article 2022
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Torres Alves, G.A. (author), 't Hart, C.M.P. (author), Morales Napoles, O. (author), Jonkman, Sebastiaan N. (author)A submerged floating tunnel (SFT) is a structure that has been proposed as an innovative solution for waterway crossings around the world. However, to this day, no SFT has been constructed yet. One of the main reasons is that there is an insufficient insight into the structural reliability of the SFT. Here, a method to assess the expected...journal article 2022
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van der Toorn, R. (author)We enhance Frobenius’ method for solving linear ordinary differential equations about regular singular points. Key to Frobenius’ approach is the exploration of the derivative with respect to a single parameter; this parameter is introduced through the powers of generalized power series. Extending this approach, we discover that tandem recurrence...journal article 2022
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Dijkstra, Y.M. (author), Schuttelaars, H.M. (author)The salinity structure in estuaries is classically described in terms of the salinity structure as well mixed, partially mixed, or salt wedge. The existing knowledge about the processes that result in such salinity structures comes from highly idealized models that are restricted to either well-mixed and partially mixed cases or subtidal salt...journal article 2021
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Barbaro, Alethea (author), Rodriguez, Nancy (author), Yoldas, H. (author), Zamponi, Nicola (author)We study a two-species cross-diffusion model that is inspired by a system of convectiondiffusion equations derived from an agent-based model on a two-dimensional discrete lattice. The latter model has been proposed to simulate gang territorial development through the use of graffiti markings. We find two energy functionals for the system that...journal article 2021
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Marynets, K. (author)We deal with a system of quasilinear fractional differential equations, subjected to the Cauchy–Nicoletti type boundary conditions. The task of explicit solution of such problems is difficult and not always solvable. Thus we suggest a suitable numerical–analytic technique that allows to construct an approximate solution of the studied...journal article 2020
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Prasse, B. (author), Van Mieghem, P.F.A. (author)The majority of epidemic models are described by non-linear differential equations which do not have a closed-form solution. Due to the absence of a closed-form solution, the understanding of the precise dynamics of a virus is rather limited. We solve the differential equations of the N-intertwined mean-field approximation of the susceptible...journal article 2020
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Keetch, Blaine (author), van Gennip, Y. (author)The Max-Cut problem is a well known combinatorial optimization problem. In this paper we describe a fast approximation method. Given a graph G, we want to find a cut whose size is maximal among all possible cuts. A cut is a partition of the vertex set of G into two disjoint subsets. For an unweighted graph, the size of the cut is the number...journal article 2019