Relevant bibliographies by topics / Probabilistic interpretation of partial differential equations

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Probabilistic interpretation of partial differential equations'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Probabilistic interpretation of partial differential equations"

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Zhu, Qingfeng, and Yufeng Shi. "Mean-Field Forward-Backward Doubly Stochastic Differential Equations and Related Nonlocal Stochastic Partial Differential Equations." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/194341.

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Mean-field forward-backward doubly stochastic differential equations (MF-FBDSDEs) are studied, which extend many important equations well studied before. Under some suitable monotonicity assumptions, the existence and uniqueness results for measurable solutions are established by means of a method of continuation. Furthermore, the probabilistic interpretation for the solutions to a class of nonlocal stochastic partial differential equations (SPDEs) combined with algebra equations is given.
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Wu, Zhen, and Ruimin Xu. "Probabilistic interpretation for Sobolev solutions of McKean–Vlasov partial differential equations." Statistics & Probability Letters 145 (February 2019): 273–83. http://dx.doi.org/10.1016/j.spl.2018.10.001.

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Harraj, N., Y. Ouknine, and I. Turpin. "Double-barriers-reflected BSDEs with jumps and viscosity solutions of parabolic integrodifferential PDEs." Journal of Applied Mathematics and Stochastic Analysis 2005, no. 1 (2005): 37–53. http://dx.doi.org/10.1155/jamsa.2005.37.

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We give a probabilistic interpretation of the viscosity solutions of parabolic integrodifferential partial equations with two obstacles via the solutions of forward-backward stochastic differential equations with jumps.
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PARDOUX, E., F. PRADEILLES, and Z. RAO. "Probabilistic interpretation of a system of semi-linear parabolic partial differential equations." Annales de l'Institut Henri Poincare (B) Probability and Statistics 33, no. 4 (1997): 467–90. http://dx.doi.org/10.1016/s0246-0203(97)80101-x.

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Zhu, Bo, and Baoyan Han. "Stochastic PDEs and Infinite Horizon Backward Doubly Stochastic Differential Equations." Journal of Applied Mathematics 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/582645.

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We give a sufficient condition on the coefficients of a class of infinite horizon BDSDEs, under which the infinite horizon BDSDEs have a unique solution for any given square integrable terminal values. We also show continuous dependence theorem and convergence theorem for this kind of equations. A probabilistic interpretation for solutions to a class of stochastic partial differential equations is given.
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Matoussi, Anis, Wissal Sabbagh, and Chao Zhou. "The obstacle problem for semilinear parabolic partial integro-differential equations." Stochastics and Dynamics 15, no. 01 (2014): 1550007. http://dx.doi.org/10.1142/s0219493715500070.

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This paper presents a probabilistic interpretation for the weak Sobolev solution of the obstacle problem for semilinear parabolic partial integro-differential equations (PIDEs). The results of Léandre [32] concerning the homeomorphic property for the solution of SDEs with jumps are used to construct random test functions for the variational equation for such PIDEs. This results in the natural connection with the associated Reflected Backward Stochastic Differential Equations with jumps (RBSDEs), namely Feynman–Kac's formula for the solution of the PIDEs. Moreover, it gives an application to the pricing and hedging of contingent claims with constraints in the wealth or portfolio processes in financial markets including jumps.
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Kolokoltsov, Vassili, Feng Lin, and Aleksandar Mijatović. "Monte carlo estimation of the solution of fractional partial differential equations." Fractional Calculus and Applied Analysis 24, no. 1 (2021): 278–306. http://dx.doi.org/10.1515/fca-2021-0012.

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Abstract The paper is devoted to the numerical solutions of fractional PDEs based on its probabilistic interpretation, that is, we construct approximate solutions via certain Monte Carlo simulations. The main results represent the upper bound of errors between the exact solution and the Monte Carlo approximation, the estimate of the fluctuation via the appropriate central limit theorem (CLT) and the construction of confidence intervals. Moreover, we provide rates of convergence in the CLT via Berry-Esseen type bounds. Concrete numerical computations and illustrations are included.
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REN, YONG, and XILIANG FAN. "REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY A LÉVY PROCESS." ANZIAM Journal 50, no. 4 (2009): 486–500. http://dx.doi.org/10.1017/s1446181109000303.

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AbstractIn this paper, we deal with a class of reflected backward stochastic differential equations (RBSDEs) corresponding to the subdifferential operator of a lower semi-continuous convex function, driven by Teugels martingales associated with a Lévy process. We show the existence and uniqueness of the solution for RBSDEs by means of the penalization method. As an application, we give a probabilistic interpretation for the solutions of a class of partial differential-integral inclusions.
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Wu, Zhen, and Zhiyong Yu. "Probabilistic interpretation for a system of quasilinear parabolic partial differential equation combined with algebra equations." Stochastic Processes and their Applications 124, no. 12 (2014): 3921–47. http://dx.doi.org/10.1016/j.spa.2014.07.013.

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Hu, Ying. "Probabilistic interpretation of a system of quasilinear elliptic partial differential equations under Neumann boundary conditions." Stochastic Processes and their Applications 48, no. 1 (1993): 107–21. http://dx.doi.org/10.1016/0304-4149(93)90109-h.

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Dissertations / Theses on the topic "Probabilistic interpretation of partial differential equations"

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Gilmour, Isla. "Nonlinear model evaluation : ɩ-shadowing, probabilistic prediction and weather forecasting". Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.298797.

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Physical processes are often modelled using nonlinear dynamical systems. If such models are relevant then they should be capable of demonstrating behaviour observed in the physical process. In this thesis a new measure of model optimality is introduced: the distribution of ɩ-shadowing times defines the durations over which there exists a model trajectory consistent with the observations. By recognising the uncertainty present in every observation, including the initial condition, ɩ-shadowing distinguishes model sensitivity from model error; a perfect model will always be accepted as optimal. The traditional root mean square measure may confuse sensitivity and error, and rank an imperfect model over a perfect one. In a perfect model scenario a good variational assimilation technique will yield an ɩ-shadowing trajectory but this is not the case given an imperfect model; the inability of the model to ɩ-shadow provides information on model error, facilitating the definition of an alternative assimilation technique and enabling model improvement. While the ɩ-shadowing time of a model defines a limit of predictability, it does not validate the model as a predictor. Ensemble forecasting provides the preferred approach for evaluating the uncertainty in predictions, yet questions remain as to how best to construct ensembles. The formation of ensembles is contrasted in perfect and imperfect model scenarios in systems ranging from the analytically tractable to the Earth's atmosphere, thereby addressing the question of whether the apparent simplicity often observed in very high-dimensional weather models fails `even in or only in' low-dimensional chaotic systems. Simple tests of the consistency between constrained ensembles and their methods of formulation are proposed and illustrated. Specifically, the commonly held belief that initial uncertainties in the state of the atmosphere of realistic amplitude behave linearly for two days is tested in operational numerical weather prediction models and found wanting: nonlinear effects are often important on time scales of 24 hours. Through the kind consideration of the European Centre for Medium-range Weather Forecasting, the modifications suggested by this are tested in an operational model.
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Sabbagh, Wissal. "Some Contributions on Probabilistic Interpretation For Nonlinear Stochastic PDEs." Thesis, Le Mans, 2014. http://www.theses.fr/2014LEMA1019/document.

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L'objectif de cette thèse est l'étude de la représentation probabiliste des différentes classes d'EDPSs non-linéaires(semi-linéaires, complètement non-linéaires, réfléchies dans un domaine) en utilisant les équations différentielles doublement stochastiques rétrogrades (EDDSRs). Cette thèse contient quatre parties différentes. Nous traitons dans la première partie les EDDSRs du second ordre (2EDDSRs). Nous montrons l'existence et l'unicité des solutions des EDDSRs en utilisant des techniques de contrôle stochastique quasi- sure. La motivation principale de cette étude est la représentation probabiliste des EDPSs complètement non-linéaires. Dans la deuxième partie, nous étudions les solutions faibles de type Sobolev du problème d'obstacle pour les équations à dérivées partielles inteégro-différentielles (EDPIDs). Plus précisément, nous montrons la formule de Feynman-Kac pour l'EDPIDs par l'intermédiaire des équations différentielles stochastiques rétrogrades réfléchies avec sauts (EDSRRs). Plus précisément, nous établissons l'existence et l'unicité de la solution du problème d'obstacle, qui est considérée comme un couple constitué de la solution et de la mesure de réflexion. L'approche utilisée est basée sur les techniques de flots stochastiques développées dans Bally et Matoussi (2001) mais les preuves sont beaucoup plus techniques. Dans la troisième partie, nous traitons l'existence et l'unicité pour les EDDSRRs dans un domaine convexe D sans aucune condition de régularité sur la frontière. De plus, en utilisant l'approche basée sur les techniques du flot stochastiques nous démontrons l'interprétation probabiliste de la solution faible de type Sobolev d'une classe d'EDPSs réfléchies dans un domaine convexe via les EDDSRRs. Enfin, nous nous intéressons à la résolution numérique des EDDSRs à temps terminal aléatoire. La motivation principale est de donner une représentation probabiliste des solutions de Sobolev d'EDPSs semi-linéaires avec condition de Dirichlet nul au bord. Dans cette partie, nous étudions l'approximation forte de cette classe d'EDDSRs quand le temps terminal aléatoire est le premier temps de sortie d'une EDS d'un domaine cylindrique. Ainsi, nous donnons les bornes pour l'erreur d'approximation en temps discret. Cette partie se conclut par des tests numériques qui démontrent que cette approche est effective<br>The objective of this thesis is to study the probabilistic representation (Feynman-Kac for- mula) of different classes ofStochastic Nonlinear PDEs (semilinear, fully nonlinear, reflected in a domain) by means of backward doubly stochastic differential equations (BDSDEs). This thesis contains four different parts. We deal in the first part with the second order BDS- DEs (2BDSDEs). We show the existence and uniqueness of solutions of 2BDSDEs using quasi sure stochastic control technics. The main motivation of this study is the probabilistic representation for solution of fully nonlinear SPDEs. First, under regularity assumptions on the coefficients, we give a Feynman-Kac formula for classical solution of fully nonlinear SPDEs and we generalize the work of Soner, Touzi and Zhang (2010-2012) for deterministic fully nonlinear PDE. Then, under weaker assumptions on the coefficients, we prove the probabilistic representation for stochastic viscosity solution of fully nonlinear SPDEs. In the second part, we study the Sobolev solution of obstacle problem for partial integro-differentialequations (PIDEs). Specifically, we show the Feynman-Kac formula for PIDEs via reflected backward stochastic differentialequations with jumps (BSDEs). Specifically, we establish the existence and uniqueness of the solution of the obstacle problem, which is regarded as a pair consisting of the solution and the measure of reflection. The approach is based on stochastic flow technics developed in Bally and Matoussi (2001) but the proofs are more technical. In the third part, we discuss the existence and uniqueness for RBDSDEs in a convex domain D without any regularity condition on the boundary. In addition, using the approach based on the technics of stochastic flow we provide the probabilistic interpretation of Sobolev solution of a class of reflected SPDEs in a convex domain via RBDSDEs. Finally, we are interested in the numerical solution of BDSDEs with random terminal time. The main motivation is to give a probabilistic representation of Sobolev solution of semilinear SPDEs with Dirichlet null condition. In this part, we study the strong approximation of this class of BDSDEs when the random terminal time is the first exit time of an SDE from a cylindrical domain. Thus, we give bounds for the discrete-time approximation error.. We conclude this part with numerical tests showing that this approach is effective
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Roux, Raphaël. "Étude probabiliste de systèmes de particules en interaction : applications à la simulation moléculaire." Phd thesis, Université Paris-Est, 2010. http://tel.archives-ouvertes.fr/tel-00597479.

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Ce travail présente quelques résultats sur les systèmes de particules en interaction pour l'interprétation probabiliste des équations aux dérivées partielles, avec des applications à des questions de dynamique moléculaire et de chimie quantique. On présente notamment une méthode particulaire permettant d'analyser le processus de la force biaisante adaptative, utilisé en dynamique moléculaire pour le calcul de différences d'énergies libres. On étudie également la sensibilité de dynamiques stochastiques par rapport à un paramètre, en vue du calcul des forces dans l'approximation de Born-Oppenheimer pour rechercher l'état quantique fondamental de molécules. Enfin, on présente un schéma numérique basé sur un système de particules pour résoudre des lois de conservation scalaires, avec un terme de diffusion anormale se traduisant par une dynamique de sauts sur les particules
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Kohler, Dominic Christopher [Verfasser], Johannes [Akademischer Betreuer] Müller, Youssef [Akademischer Betreuer] Marzouk, and Albert [Akademischer Betreuer] Gilg. "State-Discrete Probabilistic Methods for Partial Differential Equations / Dominic Christopher Kohler. Gutachter: Youssef Marzouk ; Albert Gilg ; Johannes Müller. Betreuer: Johannes Müller." München : Universitätsbibliothek der TU München, 2014. http://d-nb.info/1048428710/34.

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Schmidt, Daniel. "Kinetic Monte Carlo Methods for Computing First Capture Time Distributions in Models of Diffusive Absorption." Scholarship @ Claremont, 2017. https://scholarship.claremont.edu/hmc_theses/97.

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In this paper, we consider the capture dynamics of a particle undergoing a random walk above a sheet of absorbing traps. In particular, we seek to characterize the distribution in time from when the particle is released to when it is absorbed. This problem is motivated by the study of lymphocytes in the human blood stream; for a particle near the surface of a lymphocyte, how long will it take for the particle to be captured? We model this problem as a diffusive process with a mixture of reflecting and absorbing boundary conditions. The model is analyzed from two approaches. The first is a numerical simulation using a Kinetic Monte Carlo (KMC) method that exploits exact solutions to accelerate a particle-based simulation of the capture time. A notable advantage of KMC is that run time is independent of how far from the traps one begins. We compare our results to the second approach, which is asymptotic approximations of the FPT distribution for particles that start far from the traps. Our goal is to validate the efficacy of homogenizing the surface boundary conditions, replacing the reflecting (Neumann) and absorbing (Dirichlet) boundary conditions with a mixed (Robin) boundary condition.
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Le, cavil Anthony. "Représentation probabiliste de type progressif d'EDP nonlinéaires nonconservatives et algorithmes particulaires." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLY023.

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Dans cette thèse, nous proposons une approche progressive (forward) pour la représentation probabiliste d'Equations aux Dérivées Partielles (EDP) nonlinéaires et nonconservatives, permettant ainsi de développer un algorithme particulaire afin d'en estimer numériquement les solutions. Les Equations Différentielles Stochastiques Nonlinéaires de type McKean (NLSDE) étudiées dans la littérature constituent une formulation microscopique d'un phénomène modélisé macroscopiquement par une EDP conservative. Une solution d'une telle NLSDE est la donnée d'un couple $(Y,u)$ où $Y$ est une solution d' équation différentielle stochastique (EDS) dont les coefficients dépendent de $u$ et de $t$ telle que $u(t,cdot)$ est la densité de $Y_t$. La principale contribution de cette thèse est de considérer des EDP nonconservatives, c'est-à- dire des EDP conservatives perturbées par un terme nonlinéaire de la forme $Lambda(u,nabla u)u$. Ceci implique qu'un couple $(Y,u)$ sera solution de la représentation probabiliste associée si $Y$ est un encore un processus stochastique et la relation entre $Y$ et la fonction $u$ sera alors plus complexe. Etant donnée la loi de $Y$, l'existence et l'unicité de $u$ sont démontrées par un argument de type point fixe via une formulation originale de type Feynmann-Kac<br>This thesis performs forward probabilistic representations of nonlinear and nonconservative Partial Differential Equations (PDEs), which allowto numerically estimate the corresponding solutions via an interacting particle system algorithm, mixing Monte-Carlo methods and non-parametric density estimates.In the literature, McKean typeNonlinear Stochastic Differential Equations (NLSDEs) constitute the microscopic modelof a class of PDEs which are conservative. The solution of a NLSDEis generally a couple $(Y,u)$ where $Y$ is a stochastic process solving a stochastic differential equation whose coefficients depend on $u$ and at each time $t$, $u(t,cdot)$ is the law density of the random variable $Y_t$.The main idea of this thesis is to consider this time a non-conservative PDE which is the result of a conservative PDE perturbed by a term of the type $Lambda(u, nabla u) u$. In this case, the solution of the corresponding NLSDE is again a couple $(Y,u)$, where again $Y$ is a stochastic processbut where the link between the function $u$ and $Y$ is more complicated and once fixed the law of $Y$, $u$ is determined by a fixed pointargument via an innovating Feynmann-Kac type formula
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MOMESSO, ROBERTA G. R. A. P. "Desenvolvimento e validação de um referencial metodológico para avaliação da cultura de segurança de organizações nucleares." reponame:Repositório Institucional do IPEN, 2017. http://repositorio.ipen.br:8080/xmlui/handle/123456789/28035.

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Submitted by Pedro Silva Filho (pfsilva@ipen.br) on 2017-11-22T16:34:17Z No. of bitstreams: 0<br>Made available in DSpace on 2017-11-22T16:34:17Z (GMT). No. of bitstreams: 0<br>A cultura de segurança na área nuclear é definida como o conjunto de características e atitudes da organização e dos indivíduos que fazem que, com uma prioridade insuperável, as questões relacionadas à proteção e segurança nuclear recebam a atenção assegurada pelo seu significado. Até o momento, não existem instrumentos validados que permitam avaliar a cultura de segurança na área nuclear. Em vista disso, os resultados da definição de estratégias para o seu fortalecimento e o acompanhamento do desempenho das ações de melhorias tornam-se difíceis de serem avaliados. Este trabalho teve como objetivo principal desenvolver e validar um instrumento para a avaliação da cultura de segurança de organizações nucleares, utilizando o Instituto de Pesquisas Energéticas e Nucleares como unidade de pesquisa e coleta de dados. Os indicadores e variáveis latentes do instrumento foram definidos utilizando como referência modelos de avaliação de cultura de segurança da área da saúde e área nuclear. O instrumento de coleta de dados proposto inicialmente foi submetido à avaliação por especialistas da área nuclear e, posteriormente, ao pré-teste com indivíduos que pertenciam à população pesquisada. A validação do modelo foi feita por meio da modelagem por equações estruturais utilizando o método de mínimos quadrados parciais (Partial Least Square - Structural Equation Modeling PLS-SEM), no software SmartPLS. A versão final do instrumento foi composta por quarenta indicadores distribuídos em nove variáveis latentes. O modelo de mensuração apresentou validade convergente, validade discriminante e confiabilidade e, o modelo estrutural apresentou significância estatística, demonstrando que o instrumento cumpriu adequadamente todas as etapas de validação.<br>Tese (Doutorado em Tecnologia Nuclear)<br>IPEN/T<br>Instituto de Pesquisas Energéticas e Nucleares - IPEN-CNEN/SP
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Gu, Yu. "Probabilistic Approaches to Partial Differential Equations with Large Random Potentials." Thesis, 2014. https://doi.org/10.7916/D82R3PTD.

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The thesis is devoted to an analysis of the heat equation with large random potentials in high dimensions. The size of the potential is chosen so that the large, highly oscillatory, random field is producing non-trivial effects in the asymptotic limit. We prove either homogenization, i.e., the random potential is replaced by some deterministic constant, or convergence to a stochastic partial differential equation, i.e., the random potential is replaced by some stochastic noise, depending on the correlation property. When the limit is deterministic, we provide estimates of the error between the heterogeneous and homogenized solutions when certain mixing assumption of the random potential is satisfied. We also prove a central limit type of result when the random potential is Gaussian or Poissonian. Lower dimensional and time-dependent cases are also treated. Most of the ingredients in the analysis are probabilistic, including a Feynman-Kac representation, a Brownian motion in random scenery, the Kipnis-Varadhan's method, and a quantitative martingale central limit theorem.
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Books on the topic "Probabilistic interpretation of partial differential equations"

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Graham, Carl, Thomas G. Kurtz, Sylvie Méléard, Philip E. Protter, Mario Pulvirenti, and Denis Talay. Probabilistic Models for Nonlinear Partial Differential Equations. Edited by Denis Talay and Luciano Tubaro. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0093175.

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1957-, Davies I. M., ed. Probabilistic methods in fluids: Proceedings of the Swansea 2002 workshop. World Scientific, 2003.

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1945-, Deift Percy, Levermore C. D, and Wayne C. Eugene 1956-, eds. Dynamical systems and probabilistic methods in partial differential equations: 1994 Summer Seminar on Dynamical Systems and Probabilistic Methods for Nonlinear Waves, June 20-July 1, 1994, MSRI, Berkeley, CA. American Mathematical Society, 1996.

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Bois-Reymond, Paul Du. Beiträge zur interpretation der partiellen differentialgleichungen mit drei variabeln. J. A. Barth, 1991.

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Probabilistic Methods in Fluids Workshop (2002 University of Wales Swansea). Probabilistic methods in fluids: Proceedings of the Swansea 2002 Workshop : Wales, UK, 14-19 April 2002. World Scientific, 2003.

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An introduction to stochastic differential equations. American Mathematical Society, 2013.

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E, Ozkan, ed. A method for computing unsteady flows in porous media. Longman Scientific & Technical, 1994.

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Saff, E. B., Douglas Patten Hardin, Brian Z. Simanek, and D. S. Lubinsky. Modern trends in constructive function theory: Conference in honor of Ed Saff's 70th birthday : constructive functions 2014, May 26-30, 2014, Vanderbilt University, Nashville, Tennessee. American Mathematical Society, 2016.

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(Editor), C. Graham, D. Talay (Editor), Th G. Kurtz (Editor), S. Meleard (Editor), Ph E. Protter (Editor), and M. Pulvirenti (Editor), eds. Probabilistic Models for Nonlinear Partial Differential Equations: Lectures Given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) ... 22-30, 1995 (Lecture Notes in Mathematics). Springer, 1996.

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C, Graham, Talay D, Tubaro L. 1947-, and Centro internazionale matematico estivo, eds. Probabilistic models for nonlinear partial differential equations: Lectures given at the 1st session of the Centro internazionale matematico estivo (C.I.M.E.) held in Montecatini Terme, Italy, May 22-30, 1995. Springer, 1996.

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Book chapters on the topic "Probabilistic interpretation of partial differential equations"

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Dynkin, E. "Probabilistic approach." In Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations. American Mathematical Society, 2004. http://dx.doi.org/10.1090/ulect/034/03.

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Jaffard, Stéphane. "Wavelets and analysis of partial differential equations." In Probabilistic and Stochastic Methods in Analysis, with Applications. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2791-2_1.

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Gubinelli, Massimiliano, and Nicolas Perkowski. "Probabilistic Approach to the Stochastic Burgers Equation." In Stochastic Partial Differential Equations and Related Fields. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74929-7_35.

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Fleming, W. H. "Nonlinear Partial Differential Equations -Probabilistic and Game Theoretic Methods." In Problems in Non-Linear Analysis. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-10998-0_5.

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Le Gall, Jean-François. "The Probabilistic Representation of Positive Solutions." In Spatial Branching Processes, Random Snakes and Partial Differential Equations. Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8683-3_7.

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Knopova, Victoria, and René L. Schilling. "A Probabilistic Proof of the Breakdown of Besov Regularity in L-Shaped Domains." In Stochastic Partial Differential Equations and Related Fields. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74929-7_32.

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Solem, Jan Erik, and Niels Chr Overgaard. "Region-Based Variational Problems and Normal Alignment – Geometric Interpretation of Descent PDEs." In Image Processing Based on Partial Differential Equations. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-33267-1_13.

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Talay, Denis. "Probabilistic numerical methods for partial differential equations: Elements of analysis." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0093180.

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Butkovskiy, Anatoliy, Nikolai Lepe, and Alexandr Babichev. "Continuous Media: Interpretation in Terms of Phase-Portrait Method for Dynamic Systems with Control." In Optimal Control of Partial Differential Equations II: Theory and Applications. Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-7627-8_3.

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Stroock, Daniel W. "A Probabilistic Approach to Finding Estimates for the Heat Kernel Associated with a Hörmander Form Operator." In Directions in Partial Differential Equations. Elsevier, 1987. http://dx.doi.org/10.1016/b978-0-12-195255-6.50017-9.

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Conference papers on the topic "Probabilistic interpretation of partial differential equations"

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Grigo, Constantin, and Phaedon-Stelios Koutsourelakis. "PROBABILISTIC REDUCED-ORDER MODELING FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS." In 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering. Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2017. http://dx.doi.org/10.7712/120217.5356.16731.

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Wiedemann, Thomas, Christoph Manss, Dmitriy Shutin, Achim J. Lilienthal, Valentina Karolj, and Alberto Viseras. "Probabilistic modeling of gas diffusion with partial differential equations for multi-robot exploration and gas source localization." In 2017 European Conference on Mobile Robots (ECMR). IEEE, 2017. http://dx.doi.org/10.1109/ecmr.2017.8098707.

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Luxat, J. C. "Dynamic Sensitivity Analysis of Thermal-Mechanical Deformation of a CANDU Fuel Channel." In 16th International Conference on Nuclear Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/icone16-48656.

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Abstract:
In a limiting critical break loss of coolant accident in a CANDU reactor significant degradation of heat transfer from the fuel can occur. As a result of the subsequent increase in fuel temperature it is possible that the pressure tube undergoes heat up at intermediate pressure during blowdown. This can result in ballooning deformation of the pressure tube into contact with its calandria tube. It is required that fuel channels not fail as a consequence of the thermal mechanical deformation of the pressure tube and calandria tube in such events. Dynamic sensitivity functions are derived as analytical partial differential equations derived from the equations used to model the time-dependent behavior of physical systems. The dynamic sensitivity functions can be used to propagate uncertainties using a time-dependent perturbation approach in which the variations in a set of output variables, with respect to perturbations of the input parameters, are evaluated about reference response trajectories of the input parameters and associated output variables. The dynamic sensitivity method is described in this paper and results are presented for the pressure tube heatup phase of a LOCA. These results show the importance of all key parameters with respect to specified safety evaluation criteria. The dynamic sensitivity method is applied in a probabilistic uncertainty analysis to evaluate the probability of a pressure tube experiencing creep strain deformation to contact its calandria tube during the early stages of a LOCA.
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