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Kirchner, K. (author), Willems, J. (author)A new class of fractional-order parabolic stochastic evolution equations of the form (∂t+A)γX(t)=W˙Q(t) , t∈ [0 , T] , γ∈ (0 , ∞) , is introduced, where - A generates a C -semigroup on a separable Hilbert space H and the spatiotemporal driving noise W˙ <sup>Q</sup> is the formal time derivative of an H-valued cylindrical Q-Wiener process....journal article 2023
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Titulaer, Björn (author)Spatiotemporal stochastic processes have applications in various fields, but they can be difficult to numerically approximate in a reasonable time, in particular, in the context of statistical inference for large datasets. <br/>Recently, a new approach for efficient spatiotemporal statistical modeling has been proposed, where the space-time...master thesis 2022
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Wisse, Anouk (author)This thesis treats the thin-film equation which models the film height $h$ for a viscous film in the complete wetting regime. We show existence and uniqueness to the thin-film equation with mobility m(h) = h<sup>n</sup> and mobility exponent n∈ (1,3/2)∪ (3/2,3). The thin-film equation is rewritten as an abstract Cauchy problem and usage of semi...master thesis 2022
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Kraaij, R.C. (author)We extend the Barles-Perthame procedure [4] (see also [22]) of semi-relaxed limits of viscosity solutions of Hamilton-Jacobi equations of the type f−λHf=h to the context of non-compact spaces. The convergence result allows for equations on a ‘converging sequence of spaces’ as well as Hamilton-equations written in terms of two equations in...journal article 2022
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Bierkens, G.N.J.C. (author), Verduyn Lunel, Sjoerd M. (author)The zigzag process is a variant of the telegraph process with position dependent switching intensities. A characterization of the L2-spectrum for the generator of the one-dimensional zigzag process is obtained in the case where the marginal stationary distribution on R is unimodal and the refreshment intensity is zero. Sufficient conditions...journal article 2022
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de Bos, Hidde (author)Quantum Markov Semigroups (QMS) describe the evolution of a quantum system by evolving a projection or density operator in time. QMS are generated by a generator obeying the well-known Lindblad equation. However, this is a difficult equation. Therefore, the result that the Lindblad form greatly simplifies in the case of the...bachelor thesis 2021
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Li, Vincent (author)In this thesis we present a study of quantum Markov semigroups. In particular, we mainly consider quantum Markov semigroups with detailed balance that are defined on finite-dimensional C*-algebras. They have an invariant density matrix ρ. Carlen and Maas showed that the evolution on the set of invertible density matrices that is given by such a...master thesis 2021
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Bodor, Bertalan (author), Lehtonen, Erkko (author), Quinn-Gregson, Thomas (author), Verhulst, N.D. (author)When does the complex product of a given number of subsets of a group generate the same subgroup as their union? We answer this question in a more general form by introducing HS-stability and characterising the HS-stable involution subsemigroup generated by a subset of a given involution semigroup. We study HS-stability for the special cases...journal article 2021
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Caspers, M.P.T. (author)One of the main aims of this paper is to give a large class of strongly solid compact quantum groups. We do this by using quantum Markov semigroups and noncommutative Riesz transforms. We introduce a property for quantum Markov semigroups of central multipliers on a compact quantum group which we shall call 'approximate linearity with almost...journal article 2021
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Cass, Thomas (author), Crisan, Dan (author), Dobson, P. (author), Ottobre, Michela (author)We study the long time behaviour of a large class of diffusion processes on R<sup>N</sup>, generated by second order differential operators of (possibly) degenerate type. The operators that we consider need not satisfy the Hörmander Condition (HC). Instead, they satisfy the so-called UFG condition, introduced by Herman, Lobry and Sussman in...journal article 2021
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van Neerven, J.M.A.M. (author), Veraar, M.C. (author)This paper presents a survey of maximal inequalities for stochastic convolutions in 2-smooth Banach spaces and their applications to stochastic evolution equations. This article is part of the theme issue 'Semigroup applications everywhere'.review 2020
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Agresti, A. (author), Veraar, M.C. (author)In this paper we consider L<sup>p</sup>-regularity estimates for solutions to stochastic evolution equations, which is called stochastic maximal L<sup>p</sup>-regularity. Our aim is to find a theory which is analogously to Dore's theory for deterministic evolution equations. He has shown that maximal L<sup>p</sup>-regularity is independent of...journal article 2020
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Kraaij, R.C. (author), Redig, F.H.J. (author), Versendaal, R. (author)We generalize classical large deviation theorems to the setting of complete, smooth Riemannian manifolds. We prove the analogue of Mogulskii's theorem for geodesic random walks via a general approach using viscosity solutions for Hamilton–Jacobi equations. As a corollary, we also obtain the analogue of Cramér's theorem. The approach also...journal article 2019
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Caspers, M.P.T. (author)We consider semigroup BMO-spaces associated with arbitrary von Neumann algebras and prove interpolation theorems. This extends results by Junge-Mei for the tracial case. We give examples of multipliers on free Araki-Woods algebras and in particular we L<sub>∞</sub> → BMO multipliers. We also provide L<sub>p</sub>-bounds for a natural...journal article 2019
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de Moor, Timothy (author)Wavelets are a recent development in signal processing. These kind of functions<br/>are both well-localized in time and in frequency, and so using these to transform the signal gives insight where certain frequencies are needed. The classical way of constructing wavelets, as described by Daubechies and Meyer [3,9] is only well-suited for the...master thesis 2018
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Rozendaal, J. (author), Veraar, M.C. (author)We study polynomial and exponential stability for C<sub>0</sub>-semigroups using the recently developed theory of operator-valued (L<sup>p</sup>,L<sup>q</sup>) Fourier multipliers. We characterize polynomial decay of orbits of a C<sub>0</sub>-semigroup in terms of the (L<sup>p</sup>,L<sup>q</sup>) Fourier multiplier properties of its...journal article 2018
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Rozendaal, J. (author), Veraar, M.C. (author)We study growth rates for strongly continuous semigroups. We prove that a growth rate for the resolvent on imaginary lines implies a corresponding growth rate for the semigroup if either the underlying space is a Hilbert space, or the semigroup is asymptotically analytic, or if the semigroup is positive and the underlying space is an (Formula...journal article 2018
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Bernicot, Frédéric (author), Frey, D. (author)We consider abstract Sobolev spaces of Bessel-type associated with an operator. In this work, we pursue the study of algebra properties of such functional spaces through the corresponding semigroup. As a follow-up to our previous work, we show that by making use of the property of a 'carré du champ' identity, this algebra property holds in a...journal article 2018
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Teuwen, J.J.B. (author)This dissertation consists out of two rather disjoint parts. One part concerns some results on Gaussian harmonic analysis and the other on an optimization problem in optics. In the first part we study the Ornstein–Uhlenbeck process with respect to the Gaussian measure. We focus on two areas. One is on “Gaussian” analogues of classical results in...doctoral thesis 2016
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Rozendaal, J. (author)This thesis is dedicated to the study of several aspects of the theory of functional calculus. This theory considers the combination of an operator A and a function f(z) of a variable z, resulting in an operator f(A). One then attempts to study properties of the operator f(A) in terms of properties of the operator A and the function f. A...doctoral thesis 2015
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