Tesis sobre el tema "Singular stochastic partial differential equations"
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Liu, Xuan. "Some contribution to analysis and stochastic analysis". Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:485474c0-2501-4ef0-a0bc-492e5c6c9d62.
Texto completoMartin, Jörg. "Refinements of the Solution Theory for Singular SPDEs". Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19329.
Texto completoThis thesis is concerned with the study of singular stochastic partial differential equations (SPDEs). We develop extensions to existing solution theories, present fundamental interconnections between different approaches and give applications in financial mathematics and mathematical physics. The theory of paracontrolled distribution is formulated for discrete systems, which allows us to prove a weak universality result for the parabolic Anderson model. This thesis further shows a fundamental relation between Hairer's modelled distributions and paraproducts: The space of modelled distributions can be characterized completely by using paraproducts. This can be seen a generalization of the Fourier description of Hölder spaces. Finally, we prove the existence of solutions to the stochastic Schrödinger equation on the full space and provide an application of Hairer's theory to option pricing.
Barrasso, Adrien. "Decoupled mild solutions of deterministic evolution problemswith singular or path-dependent coefficients, represented by backward SDEs". Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLY009/document.
Texto completoThis thesis introduces a new notion of solution for deterministic non-linear evolution equations, called decoupled mild solution.We revisit the links between Markovian Brownian Backward stochastic differential equations (BSDEs) and parabolic semilinear PDEs showing that under very mild assumptions, the BSDEs produce a unique decoupled mild solution of some PDE.We extend this result to many other deterministic equations such asPseudo-PDEs, Integro-PDEs, PDEs with distributional drift or path-dependent(I)PDEs. The solutions of those equations are represented throughBSDEs which may either be without driving martingale, or drivenby cadlag martingales. In particular this thesis solves the so calledidentification problem, which consists, in the case of classical Markovian Brownian BSDEs, to give an analytical meaning to the second component Z ofthe solution (Y,Z) of the BSDE. In the literature, Y generally determinesa so called viscosity solution and the identification problem is only solved when this viscosity solution has a minimal regularity.Our method allows to treat this problem even in the case of general (even non-Markovian) BSDEs with jumps
Barrasso, Adrien. "Decoupled mild solutions of deterministic evolution problemswith singular or path-dependent coefficients, represented by backward SDEs". Electronic Thesis or Diss., Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLY009.
Texto completoThis thesis introduces a new notion of solution for deterministic non-linear evolution equations, called decoupled mild solution.We revisit the links between Markovian Brownian Backward stochastic differential equations (BSDEs) and parabolic semilinear PDEs showing that under very mild assumptions, the BSDEs produce a unique decoupled mild solution of some PDE.We extend this result to many other deterministic equations such asPseudo-PDEs, Integro-PDEs, PDEs with distributional drift or path-dependent(I)PDEs. The solutions of those equations are represented throughBSDEs which may either be without driving martingale, or drivenby cadlag martingales. In particular this thesis solves the so calledidentification problem, which consists, in the case of classical Markovian Brownian BSDEs, to give an analytical meaning to the second component Z ofthe solution (Y,Z) of the BSDE. In the literature, Y generally determinesa so called viscosity solution and the identification problem is only solved when this viscosity solution has a minimal regularity.Our method allows to treat this problem even in the case of general (even non-Markovian) BSDEs with jumps
Hashemi, Seyed Naser. "Singular perturbations in coupled stochastic differential equations". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ65244.pdf.
Texto completoDareiotis, Anastasios Constantinos. "Stochastic partial differential and integro-differential equations". Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/14186.
Texto completoElton, Daniel M. "Hyperbolic partial differential equations with singular coefficients". Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.389210.
Texto completoHofmanová, Martina. "Degenerate parabolic stochastic partial differential equations". Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2013. http://tel.archives-ouvertes.fr/tel-00916580.
Texto completoMatetski, Kanstantsin. "Discretisations of rough stochastic partial differential equations". Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/81460/.
Texto completoSpantini, Alessio. "Preconditioning techniques for stochastic partial differential equations". Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/82507.
Texto completoThis thesis was scanned as part of an electronic thesis pilot project.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 149-155).
This thesis is about preconditioning techniques for time dependent stochastic Partial Differential Equations arising in the broader context of Uncertainty Quantification. State-of-the-art methods for an efficient integration of stochastic PDEs require the solution field to lie on a low dimensional linear manifold. In cases when there is not such an intrinsic low rank structure we must resort on expensive and time consuming simulations. We provide a preconditioning technique based on local time stretching capable to either push or keep the solution field on a low rank manifold with substantial reduction in the storage and the computational burden. As a by-product we end up addressing also classical issues related to long time integration of stochastic PDEs.
by Alessio Spantini.
S.M.
Prerapa, Surya Mohan. "Projection schemes for stochastic partial differential equations". Thesis, University of Southampton, 2009. https://eprints.soton.ac.uk/342800/.
Texto completoZhang, Qi. "Stationary solutions of stochastic partial differential equations and infinite horizon backward doubly stochastic differential equations". Thesis, Loughborough University, 2008. https://dspace.lboro.ac.uk/2134/34040.
Texto completoMu, Tingshu. "Backward stochastic differential equations and applications : optimal switching, stochastic games, partial differential equations and mean-field". Thesis, Le Mans, 2020. http://www.theses.fr/2020LEMA1023.
Texto completoThis thesis is related to Doubly Reflected Backward Stochastic Differential Equations (DRBSDEs) with two obstacles and their applications in zero-sum stochastic switching games, systems of partial differential equations, mean-field problems.There are two parts in this thesis. The first part deals with optimal stochastic switching and is composed of two works. In the first work we prove the existence of the solution of a system of DRBSDEs with bilateral interconnected obstacles in a probabilistic framework. This problem is related to a zero-sum switching game. Then we tackle the problem of the uniqueness of the solution. Finally, we apply the obtained results and prove that, without the usual monotonicity condition, the associated PDE system has a unique solution in viscosity sense. In the second work, we also consider a system of DRBSDEs with bilateral interconnected obstacles in the markovian framework. The difference between this work and the first one lies in the fact that switching does not work in the same way. In this second framework, when switching is operated, the system is put in the following state regardless of which player decides to switch. This difference is fundamental and largely complicates the problem of the existence of the solution of the system. Nevertheless, in the Markovian framework we show this existence and give a uniqueness result by the Perron’s method. Later on, two particular switching games are analyzed.In the second part we study a one-dimensional Reflected BSDE with two obstacles of mean-field type. By the fixed point method, we show the existence and uniqueness of the solution in connection with the integrality of the data
Athreya, Siva. "Probability and semilinear partial differential equations /". Thesis, Connect to this title online; UW restricted, 1998. http://hdl.handle.net/1773/5799.
Texto completoLattimer, Timothy Richard Bislig. "Singular partial integro-differential equations arising in thin aerofoil theory". Thesis, University of Southampton, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.243192.
Texto completoMphaka, Mphaka Joane Sankoela. "Partial singular integro-differential equations models for dryout in boilers". Thesis, University of Southampton, 2000. https://eprints.soton.ac.uk/50627/.
Texto completoHsu, Yueh-Sheng. "On the random Schrödinger operators in the continuous setting". Electronic Thesis or Diss., Université Paris sciences et lettres, 2024. http://www.theses.fr/2024UPSLD009.
Texto completoThis thesis studies the random Schrödinger operators in continuous setting, particularly those with Gaussian white noise potential. The definition of such differential operators is generally non-trivial and necessitates renormalization in dimensions d ≥ 2. We first present a general framework to translate the problem of operator construction into stochastic PDEs. This approach enables us to define the operator at stake and establishes its self-adjointness, as well as to investigate its spectrum.Subsequently, we proceed to study the continuous Anderson Hamiltonian under two distinct spatial settings: first on a bounded box with side length L with zero Dirichlet boundary condition for dimensions d ≤ 3, and second on the full Euclidean space Rd, for d ∈ {2, 3}. In the former case, the operator admits eigenvalues λn,L, for which we identify the almost sure asymptotic as L → ∞. This asymptotic aligns with previous findings in the literature for dimension 1 and 2, while our result in dimension 3 is new. In the latter case, we propose a new construction technique employing the solution theory to the associated parabolic equation which allows to prove self-adjointness and show that the spectrum equals to R almost surely. This approach reconfirms the recently established result in dimension 2, but our construction seems to be more elementary; for dimension 3, our result is new.Lastly, we present an ongoing project addressing the case where a uniform magnetic field is applied to the system : this leads to the study of Landau Hamiltonian perturbed by the white noise potential. Our objective is to define the operator on full space R² without resorting to sophisticated renormalization theory. However, the unboundedness of white noise on R² poses additional technical challenges. To overcome this, the usage of Faris-Lavine theorem is discussed
Pätz, Torben [Verfasser]. "Segmentation of Stochastic Images using Stochastic Partial Differential Equations / Torben Pätz". Bremen : IRC-Library, Information Resource Center der Jacobs University Bremen, 2012. http://d-nb.info/1035219735/34.
Texto completoLing, Chengcheng [Verfasser]. "Stochastic differential equations with singular drifts and multiplicative noises / Chengcheng Ling". Bielefeld : Universitätsbibliothek Bielefeld, 2020. http://d-nb.info/1206592184/34.
Texto completoAksoy, Umit. "Schwarz Problem For Complex Partial Differential Equations". Phd thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/3/12607977/index.pdf.
Texto completoPak, Alexey. "Stochastic partial differential equations with coefficients depending on VaR". Thesis, University of Warwick, 2017. http://wrap.warwick.ac.uk/93458/.
Texto completoRINALDI, PAOLO. "A Novel Perturbative Approach to Stochastic Partial Differential Equations". Doctoral thesis, Università degli studi di Pavia, 2022. http://hdl.handle.net/11571/1447824.
Texto completoCheung, Ka Chun. "Meshless algorithm for partial differential equations on open and singular surfaces". HKBU Institutional Repository, 2016. https://repository.hkbu.edu.hk/etd_oa/278.
Texto completoMcKay, Steven M. "Brownian Motion Applied to Partial Differential Equations". DigitalCommons@USU, 1985. https://digitalcommons.usu.edu/etd/6992.
Texto completoEmereuwa, Chigoziem A. "Homogenization of stochastic partial differential equations in perforated porous media". Thesis, University of Pretoria, 2019. http://hdl.handle.net/2263/77812.
Texto completoThesis (PhD)--University of Pretoria, 2019.
Mathematics and Applied Mathematics
PhD
Unrestricted
o, Perdomo Rafael Antonio. "Optimal control of stochastic partial differential equations in Banach spaces". Thesis, University of York, 2010. http://etheses.whiterose.ac.uk/1112/.
Texto completoIgnatyev, Oleksiy. "The Compact Support Property for Hyperbolic SPDEs: Two Contrasting Equations". [Kent, Ohio] : Kent State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=kent1216323351.
Texto completoTitle from PDF t.p. (viewed Nov. 10, 2009). Advisor: Hassan Allouba. Keywords: stochastic partial differential equations; compact support property. Includes bibliographical references (p. 30).
Mai, Thanh Tan [Verfasser]. "Stochastic partial differential equations corresponding to time-inhomogeneous evolution equations / Thanh Tan Mai". München : Verlag Dr. Hut, 2012. http://d-nb.info/1029399719/34.
Texto completoTerrone, Gabriele. "Singular Perturbation and Homogenization Problems in Control Theory, Differential Games and fully nonlinear Partial Differential Equations". Doctoral thesis, Università degli studi di Padova, 2008. http://hdl.handle.net/11577/3426271.
Texto completovon, Schwerin Erik. "Convergence rates of adaptive algorithms for stochastic and partial differential equations". Licentiate thesis, KTH, Numerical Analysis and Computer Science, NADA, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-302.
Texto completoSchwerin, Erik von. "Convergence rates of adaptive algorithms for stochastic and partial differential equations /". Stockholm, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-302.
Texto completoLeonhard, Claudine [Verfasser]. "Derivative-free numerical schemes for stochastic partial differential equations / Claudine Leonhard". Lübeck : Zentrale Hochschulbibliothek Lübeck, 2017. http://d-nb.info/1135168091/34.
Texto completoNeuß, Marius [Verfasser]. "Stochastic partial differential equations arising in self-organized criticality / Marius Neuß". Bielefeld : Universitätsbibliothek Bielefeld, 2021. http://d-nb.info/1231994762/34.
Texto completoLuo, Wuan Hou Thomas Y. "Wiener chaos expansion and numerical solutions of stochastic partial differential equations /". Diss., Pasadena, Calif. : Caltech, 2006. http://resolver.caltech.edu/CaltechETD:etd-05182006-173710.
Texto completoCartwright, Madeleine Clare. "Collective coordinates approach for travelling waves in stochastic partial differential equations". Thesis, The University of Sydney, 2021. https://hdl.handle.net/2123/25942.
Texto completoYang, Juan. "Invariant measures for stochastic partial differential equations and splitting-up method for stochastic flows". Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/invariant-measures-for-stochastic-partial-differential-equations-and-splittingup-method-for-stochastic-flows(36b3d40a-5094-4364-8732-12324ef3a72f).html.
Texto completoWang, Xince. "Quasilinear PDEs and forward-backward stochastic differential equations". Thesis, Loughborough University, 2015. https://dspace.lboro.ac.uk/2134/17383.
Texto completoJin, Chao. "Parallel domain decomposition methods for stochastic partial differential equations and analysis of nonlinear integral equations". Connect to online resource, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3256468.
Texto completoPhilipowski, Robert. "Stochastic interacting particle systems and nonlinear partial differential equations from fluid mechanics". [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=986005622.
Texto completovon, Schwerin Erik. "Adaptivity for Stochastic and Partial Differential Equations with Applications to Phase Transformations". Doctoral thesis, KTH, Numerisk Analys och Datalogi, NADA, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4477.
Texto completoQC 20100823
Schwerin, Erik von. "Adaptivity for stochastic and partial differential equations with applications to phase transformations /". Stockholm : Numerisk analys och datalogi, Kungliga Tekniska högskolan, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4477.
Texto completoWieland, Bernhard [Verfasser]. "Reduced basis methods for partial differential equations with stochastic influences / Bernhard Wieland". Ulm : Universität Ulm. Fakultät für Mathematik und Wirtschaftswissenschaften, 2013. http://d-nb.info/1038004780/34.
Texto completoSturm, Anja Karin. "On spatially structured population processes and relations to stochastic partial differential equations". Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249618.
Texto completoStanciulescu, Vasile Nicolae. "Selected topics in Dirichlet problems for linear parabolic stochastic partial differential equations". Thesis, University of Leicester, 2010. http://hdl.handle.net/2381/8271.
Texto completoYeadon, Cyrus. "Approximating solutions of backward doubly stochastic differential equations with measurable coefficients using a time discretization scheme". Thesis, Loughborough University, 2015. https://dspace.lboro.ac.uk/2134/20643.
Texto completoLeahy, James-Michael. "On parabolic stochastic integro-differential equations : existence, regularity and numerics". Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/10569.
Texto completoYang, Weiye. "Stochastic analysis and stochastic PDEs on fractals". Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:43a7af74-c531-424a-9f3d-4277138affbb.
Texto completoYang, Jie. "Solving Partial Differential Equations by Taylor Meshless Method". Thesis, Université de Lorraine, 2018. http://www.theses.fr/2018LORR0032/document.
Texto completoBased on Taylor Meshless Method (TMM), the aim of this thesis is to develop a simple, robust, efficient and accurate numerical method which is capable of solving large scale engineering problems and to provide a new idea for the follow-up study on meshless methods. To this end, the influence of the key factors in TMM has been studied by solving three-dimensional and non-linear Partial Differential Equations (PDEs). The main idea of TMM is to use high order polynomials as shape functions which are approximated solutions of the PDE and the discretization concerns only the boundary. To solve the unknown coefficients, boundary conditions are accounted by collocation procedures associated with least-square method. TMM that needs only boundary collocation without integration process, is a true meshless method. The main contributions of this thesis are as following: 1) Based on TMM, a general and efficient algorithm has been developed for solving three-dimensional PDEs; 2) Three coupling techniques in piecewise resolutions have been discussed and tested in cases of large-scale problems, including least-square collocation method and two coupling methods based on Lagrange multipliers; 3) A general numerical method for solving non-linear PDEs has been proposed by combining Newton Method, TMM and Automatic Differentiation technique; 4) To apply TMM for solving problems with singularities, the singular solutions satisfying the control equation are introduced as complementary shape functions, which provides a theoretical basis for solving singular problems
Ali, Zakaria Idriss. "Existence result for a class of stochastic quasilinear partial differential equations with non-standard growth". Diss., University of Pretoria, 2010. http://hdl.handle.net/2263/29519.
Texto completoDissertation (MSc)--University of Pretoria, 2010.
Mathematics and Applied Mathematics
unrestricted
Soomro, Inayatullah. "Mathematical and computational modelling of stochastic partial differential equations applied to advanced methods". Thesis, University of Central Lancashire, 2016. http://clok.uclan.ac.uk/20422/.
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