Auswahl der wissenschaftlichen Literatur zum Thema „Equations aux dérivées partielles stochastiques singulières“
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Zeitschriftenartikel zum Thema "Equations aux dérivées partielles stochastiques singulières"
Lefebvre, Mario. „Solutions de similitude d'un jeu différentiel stochastique“. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées Volume 5, Special Issue TAM... (29.11.2006). http://dx.doi.org/10.46298/arima.1864.
Der volle Inhalt der QuelleVan den Berg, Imme, und Elsa Amaro. „Nearly recombining processes and the calculation of expectations“. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées Volume 9, 2007 Conference in... (05.09.2008). http://dx.doi.org/10.46298/arima.1907.
Der volle Inhalt der QuelleDissertationen zum Thema "Equations aux dérivées partielles stochastiques singulières"
Popier, Alexandre François Roland. „Equations différentielles stochastiques rétrogrades avec condition finale singulière“. Aix-Marseille 1, 2004. http://www.theses.fr/2004AIX11037.
Der volle Inhalt der QuelleDiop, Mamadou Abdoul. „Equations aux dérivées partielles stochastiques et homogénéisation“. Aix-Marseille 1, 2003. http://www.theses.fr/2003AIX11017.
Der volle Inhalt der QuelleThis thesis is devoted to some problems connected to the theory of homogenization of random parabolic operators with large potential. It is assumed that the said operators have a periodic spatial microstructure whose characteristics are rapidly oscillating stationary random process in time. Two different cases of non diffusive scaling are addressed. Namely, the case when the oscillation in time is faster than that in spatial variables and the opposite case when the time oscillation is slower than that the spatial one. It is shown that in the former case, under certain mixing conditions,the corresponding Cauchy problem admits homogenization and its solution converges in probability to a solution of a deterministic semilinear operator. In the latter case the limit equation is a stochastic partial differential equation. Here a solution of the original Cauchy problem converges in law in the energy functional space, while con vergence in probability does not takes place. The thesis consists of an introduction and three different parts. In the introduction we give an elementary presentation of the basic ideas in the homogenization theory. The first chapter, deals with the results contained in this thesis. In the second chapter the operators with Markov driving processes are considered. In the second part the operators with non Markov coefficients are investigated
Hsu, 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.
Der volle Inhalt der QuelleThis 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
Debbi, Latifa. „Equations aux dérivées partielles déterministes et stochastiques avec opérateurs fractionnaires“. Nancy 1, 2006. http://www.theses.fr/2006NAN10046.
Der volle Inhalt der QuelleThis thesis treats application of fractional calculus in stochastic analysis. In the first part, the definition of the the multidimensional Riesz-Feller fractional differential operator is extended to higher order. The operator obtained generalizes several known fractional differential and pseudodifferential operators. High order fractional Fokker-Plank equations are studied in both the probabilistic and the quasiprobabilistic approaches. In particular, the solutions are represented via stable Lévy processes and generalization of Airy's function. In the second part, onedimensional stochastic fractional partial differential equations perturbed by space-time white noise are considered. The existence and the uniqueness of field solutions and of L2solutions are proved under different Lipschtz conditions. Spatial and temporal Hölder exponents of the field solutions are obtained. Further, equivalence between several definitions of L2solutions is proven. In particular, Fourier transform is used to give meaning to some stochastic fractional partial differential equations
Zhang, Jing. „Les équations aux dérivées partielles stochastiques avec obstacle“. Thesis, Evry-Val d'Essonne, 2012. http://www.theses.fr/2012EVRY0020/document.
Der volle Inhalt der QuelleThis thesis deals with quasilinear Stochastic Partial Differential Equations (in short SPDE). It is divided into two parts, the first part concerns the obstacle problem for quasilinear SPDE and the second part solves quasilinear SPDE driven by G-Brownian motion. In the first part we begin with the existence and uniqueness result for the obstacle problem of quasilinear stochastic partial differential equations (in short OSPDE). Our method is based on analytical technics coming from the parabolic potential theory. The solution is expressed as a pair (u, v) where u is a predictable continuous process which takes values in a proper Sobolev space and v is a random regular measure satisfying minimal Skohorod condition. Then we prove a maximum principle for a local solution of quasilinear stochastic partial differential equations with obstacle. The proofs are based on a version of Itô’s formula and estimates for the positive part of a local solution which is negative on the lateral boundary. The objective of the second part is to study the well-posedness of stochastic partial differential equations driven by G-Brownian motion in the framework of sublinear expectation spaces. One can also establish an Itô formula for the solution and a comparison theorem
Riviere, Olivier. „Equations différentielles stochastiques progressives rétrogrades couplées : équations aux dérivées partielles et discrétisation“. Phd thesis, Université René Descartes - Paris V, 2005. http://tel.archives-ouvertes.fr/tel-00011231.
Der volle Inhalt der QuelleRivière, Olivier. „Equations différentielles stochastiques progressives rétrogrades couplées : équations aux dérivées partielles et discrétisation“. Paris 5, 2005. http://www.theses.fr/2005PA05S028.
Der volle Inhalt der QuelleThis thesis deals with the forward backward stochastic differential equations, in particular those with a coefficient of progressive diffusion which depends on all unknowns of the problem. We propose an original way to get onto this subject, letting us to reobtain some classical results of existence and uniqueness in the spirit of Pardoux-Tang and Yong's results, and to find a probabilistic representation of a new class of parabolic PDE, in which derivation coefficient of order 2 depends on the gradient of the solution. We also propose an iterative discretization scheme. We prove its convergence and give an evaluation of the error on a particular example
Carrizo, Vergara Ricardo. „Développement de modèles géostatistiques à l’aide d’équations aux dérivées partielles stochastiques“. Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLEM062/document.
Der volle Inhalt der QuelleThis dissertation presents theoretical advances in the application of the Stochastic Partial Differential Equation (SPDE) approach in Geostatistics. This recently developed approach consists in interpreting a regionalised data-set as a realisation of a Random Field satisfying a SPDE. Within the theoretical framework of Generalized Random Fields, the influence of a linear SPDE over the covariance structure of its potential solutions can be studied with a great generality. A criterion of existence and uniqueness of stationary solutions for a wide-class of linear SPDEs has been obtained, together with an expression for the related spectral measures. These results allow to develop spatio-temporal covariance models presenting non-trivial properties through the analysis of evolution equations presenting a fractional temporal derivative order. Suitable parametrizations of such models allow to control their separability, symmetry and separated space-time regularities. Results concerning stationary solutions for physically inspired SPDEs such as the Heat equation and the Wave equation are also presented. A method of non-conditional simulation adapted to these models is then studied. This method is based on the computation of an approximation of the Fourier Transform of the field, and it can be implemented efficiently thanks to the Fast Fourier Transform algorithm. The convergence of this method has been theoretically proven in suitable weak and strong senses. This method is applied to numerically solve the SPDEs studied in this work. Illustrations of models presenting non-trivial properties and related to physically driven equations are then given
Fedrizzi, Ennio. „Partial differential equations and noise“. Paris 7, 2012. http://www.theses.fr/2012PA077176.
Der volle Inhalt der QuelleIn this work we present examples of the effects of noise on the solution of a partial differential equation in three different settings. We first consider random initial conditions for two nonlinear dispersive partial differential equations, the nonlinear Schrodinger equation and the Korteweg - de Vries equation, and analyze their effects on some special solutions, the soliton solutions. The second case considered is a linear PDE, the wave equation, with random initial conditions. We show that special random initial conditions allow to I substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, where we will show that the addition of a multiplicative noise term forbids the blow up of solutions, under very weak hypothesis for which we have finite-time blow up of solutions in the deterministic case
Piozin, Lambert. „Quelques résultats sur les équations rétrogrades et équations aux dérivées partielles stochastiques avec singularités“. Thesis, Le Mans, 2015. http://www.theses.fr/2015LEMA1004/document.
Der volle Inhalt der QuelleThis thesis is devoted to the study of some problems in the field of backward stochastic differential equations (BSDE), and their applications to partial differential equations.In the first chapter, we introduce the notion of backward doubly stochastic differential equations (BDSDE) with singular terminal condition. A first work consists to study the case of BDSDE with monotone generator. We then obtain existing result by an approximating scheme built considering a truncation of the terminal condition. The last part of this chapter aim to establish the link with stochastic partial differential equations, using a weak solution approach developed by Bally, Matoussi in 2001.The second chapter is devoted to the BSDEs with singular terminal conditions and jumps. As in the previous chapter the tricky part will be to prove continuity in T. We formulate sufficient conditions on the jumps in order to obtain it. A section is then dedicated to establish a link between a minimal solution of our BSDE and partial integro-differential equations.The last chapter is dedicated to doubly reflected second order backward stochastic differential equations (2DRBSDE). We have been looking to establish existence and uniqueness for such equations. In order to obtain this, we had to focus first on the upper reflection problem for 2BSDEs. We combined then these results to those already existing to give a well-posedness context to 2DRBSDE. Uniqueness is established as a straight consequence of a representation property. Existence is obtained using shifted spaces, and regular conditional probability distributions. A last part is then consecrated to the link with some Dynkin games and Israeli options
Bücher zum Thema "Equations aux dérivées partielles stochastiques singulières"
1961-, Dalang Robert C., Khoshnevisan Davar und Rassoul-Agha Firas, Hrsg. A minicourse on stochastic partial differential equations. Berlin: Springer, 2009.
Den vollen Inhalt der Quelle finden1961-, Dalang Robert C., Khoshnevisan Davar und Rassoul-Agha Firas, Hrsg. A minicourse on stochastic partial differential equations. Berlin: Springer, 2009.
Den vollen Inhalt der Quelle finden1961-, Dalang Robert C., Khoshnevisan Davar und Rassoul-Agha Firas, Hrsg. A minicourse on stochastic partial differential equations. Berlin: Springer, 2009.
Den vollen Inhalt der Quelle findenGiuseppe, Da Prato, und Tubaro L. 1947-, Hrsg. Stochastic partial differential equations and applications. New York: Marcel Dekker, 2002.
Den vollen Inhalt der Quelle findenGiuseppe, Da Prato, und Tubaro L. 1947-, Hrsg. Stochastic partial differential equations and applications II: Proceedings of a conference held in Trento, Italy, February 1-6, 1988. Berlin: Springer-Verlag, 1989.
Den vollen Inhalt der Quelle findenKhoshnevisan, Davar, Robert Dalang, Carl Mueller und Firas Rassoul-Agha. Minicourse on Stochastic Partial Differential Equations. Springer London, Limited, 2008.
Den vollen Inhalt der Quelle findenPrato, Giuseppe Da, und Luciano Tubaro. Stochastic Partial Differential Equations and Applications - VII. Taylor & Francis Group, 2005.
Den vollen Inhalt der Quelle findenStochastic Partial Differential Equations and Applications - VII. Taylor & Francis Group, 2017.
Den vollen Inhalt der Quelle finden(Editor), Giuseppe Da Prato, und Luciano Tubaro (Editor), Hrsg. Stochastic Partial Differential Equations and Applications - VII (Lecture Notes in Pure and Applied Mathematics). Chapman & Hall/CRC, 2005.
Den vollen Inhalt der Quelle findenPrato, Giuseppe Da, und Luciano Tubaro. Stochastic Partial Differential Equations and Applications. Taylor & Francis Group, 2002.
Den vollen Inhalt der Quelle finden