Academic literature on the topic 'Measure-Valued stochastic processes'

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Journal articles on the topic "Measure-Valued stochastic processes"

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Panpan, Ren, and Wang Fengyu. "Stochastic analysis for measure-valued processes." SCIENTIA SINICA Mathematica 50, no. 2 (January 3, 2020): 231. http://dx.doi.org/10.1360/ssm-2019-0225.

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Dawson, Donald A., and Zenghu Li. "Stochastic equations, flows and measure-valued processes." Annals of Probability 40, no. 2 (March 2012): 813–57. http://dx.doi.org/10.1214/10-aop629.

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Dorogovtsev, Andrey A. "Stochastic flows with interaction and measure-valued processes." International Journal of Mathematics and Mathematical Sciences 2003, no. 63 (2003): 3963–77. http://dx.doi.org/10.1155/s0161171203301073.

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We consider the new class of the Markov measure-valued stochastic processes with constant mass. We give the construction of such processes with the family of the probabilities which describe the motion of single particles. We also consider examples related to stochastic flows with the interactions and the local times for such processes.
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Méléard, Sylvie, and Sylvie Roelly. "Discontinuous Measure-Valued Branching Processes and Generalized Stochastic Equations." Mathematische Nachrichten 154, no. 1 (1991): 141–56. http://dx.doi.org/10.1002/mana.19911540112.

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Dorogovtsev, Andrey A. "Measure-valued Markov processes and stochastic flows on abstract spaces." Stochastics and Stochastic Reports 76, no. 5 (October 2004): 395–407. http://dx.doi.org/10.1080/10451120422331292216.

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Mailler, Cécile, and Denis Villemonais. "Stochastic approximation on noncompact measure spaces and application to measure-valued Pólya processes." Annals of Applied Probability 30, no. 5 (October 2020): 2393–438. http://dx.doi.org/10.1214/20-aap1561.

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HE, HUI. "FLEMING–VIOT PROCESSES IN AN ENVIRONMENT." Infinite Dimensional Analysis, Quantum Probability and Related Topics 13, no. 03 (September 2010): 489–509. http://dx.doi.org/10.1142/s0219025710004127.

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We consider a new type of lookdown processes where spatial motion of each individual is influenced by an individual noise and a common noise, which could be regarded as an environment. Then a class of probability measure-valued processes on real line ℝ is constructed. The sample path properties are investigated: the values of this new type process are either purely atomic measures or absolutely continuous measures according to the existence of individual noise. When the process is absolutely continuous with respect to Lebesgue measure, we derive a new stochastic partial differential equation for the density process. At last we show that such processes also arise from normalizing a class of measure-valued branching diffusions in a Brownian medium as the classical result that Dawson–Watanabe superprocesses, conditioned to have total mass one, are Fleming–Viot superprocesses.
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Yurachkivs’kyi, A. P. "Generalization of one problem of stochastic geometry and related measure-valued processes." Ukrainian Mathematical Journal 52, no. 4 (April 2000): 600–613. http://dx.doi.org/10.1007/bf02515399.

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Feldman, Raisa E., and Srikanth K. Iyer. "Non-Gaussian Density Processes Arising from Non-Poisson Systems of Independent Brownian Motions." Journal of Applied Probability 35, no. 1 (March 1998): 213–20. http://dx.doi.org/10.1239/jap/1032192564.

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The Brownian density process is a Gaussian distribution-valued process. It can be defined either as a limit of a functional over a Poisson system of independent Brownian particles or as a solution of a stochastic partial differential equation with respect to Gaussian martingale measure. We show that, with an appropriate change in the initial distribution of the infinite particle system, the limiting density process is non-Gaussian and it solves a stochastic partial differential equation where the initial measure and the driving measure are non-Gaussian, possibly having infinite second moment.
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Feldman, Raisa E., and Srikanth K. Iyer. "Non-Gaussian Density Processes Arising from Non-Poisson Systems of Independent Brownian Motions." Journal of Applied Probability 35, no. 01 (March 1998): 213–20. http://dx.doi.org/10.1017/s0021900200014807.

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The Brownian density process is a Gaussian distribution-valued process. It can be defined either as a limit of a functional over a Poisson system of independent Brownian particles or as a solution of a stochastic partial differential equation with respect to Gaussian martingale measure. We show that, with an appropriate change in the initial distribution of the infinite particle system, the limiting density process is non-Gaussian and it solves a stochastic partial differential equation where the initial measure and the driving measure are non-Gaussian, possibly having infinite second moment.
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Dissertations / Theses on the topic "Measure-Valued stochastic processes"

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Madrid, Canales Ignacio. "Modèle de croissance cellulaire sous l’action d’un stress : Émergence d’hétérogénéité et impact de l’environnement." Electronic Thesis or Diss., Institut polytechnique de Paris, 2024. https://theses.hal.science/tel-04660317.

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Cette thèse porte sur l'analyse statistique et mathématique de la croissance cellulaire à l'échelle individuelle sous l'effet d'un stress. À partir de l'analyse des données recueillies par Sebastián Jaramillo et James Broughton sous la direction de Meriem El Karoui, nous avons construit différents modèles permettant une compréhension à différents niveaux de l'impact que la réponse hétérogène au stress génotoxique (réponse SOS) a sur la croissance d'une population de bactéries Escherichia coli. Pour modéliser la dynamique de ces populations on utilise des processus stochastiques à valeurs mesures.Nous construisons tout d'abord on construit un modèle stochastique basé sur le modèle "adder" de contrôle de la taille, étendu pour incorporer la dynamique de la réponse SOS et son effet sur la division cellulaire. Le cadre choisi est paramétrique et le modèle est ajusté par maximum de vraisemblance aux données de lignées individuelles obtenues en mother machine. Cela nous permet de comparer quantitativement les paramètres inférés dans différents environnements.Nous nous intéressons ensuite aux propriétés ergodiques d'un modèle plus général que "adder", répondant à des questions ouvertes sur son comportement en temps long. On considère un flot déterministe général et un noyau de fragmentation non nécessairement auto-similaire. Nous montrons l'existence des éléments propres. Ensuite, une $h$-transformée de Doob avec la fonction propre nous ramène à l'étude d'un processus conservatif. Enfin, en montrant une propriété de petite set pour les compacts de l'espace d'états, nous obtenons alors la convergence exponentielle du modèle.Finalement, nous considérons un modèle bitype structuré en âge modélisant la plasticité phénotypique observée dans la réponse au stress. Nous étudions la probabilité de survie et le taux de croissance de la population en environnement constant et périodique. Nous mettons en lumière un trade-off pour avoir la survie de la population, ainsi qu'une sensibilité par rapport aux paramètres du modèle qui n'est pas la même pour la probabilité de survie et pour le taux de croissance.Nous concluons avec une section indépendante, initiée durant le CEMRACS 2022. Nous étudions numériquement la propagation spatiale des populations structurés en taille modélisant le mouvement collectif de clusters de Myxobactéries à travers de systèmes d'équations de réaction-diffusion
This thesis focuses on understanding individual-scale cell growth under stress. Starting from the analysis of the data collected by Sebastián Jaramillo and James Broughton under the supervision of Meriem El Karoui, we have developed various models to comprehend the impact of the heterogeneous response to genotoxic stress (SOS response) on the growth of a Escherichia coli populations. We employ measure-values stochastic processes to model the dynamics of these populations.Firstly, we construct a stochastic model based on the "adder" size-control model, extended to incorporate the dynamics of the SOS response and its effect on cell division. The chosen framework is parametric, and the model is fitted by maximum likelihood to individual lineage data obtained in mother machine. This allows us to quantitatively compare inferred parameters in different environments.Next, we explore the ergodic properties of a more general model than the "adder," addressing open questions about its long-time behaviour. We consider a general deterministic flow and a fragmentation kernel that is not necessarily self-similar. We demonstrate the existence of eigenelements. Then, a Doob $h$-transform with the found eigenfunction reduces the problem to the study of a conservative process. Finally, by proving a "petite set" property for the compact sets of the state space, we obtain the exponential convergence.Finally, we consider a bitype age-structured model capturing the phenotypic plasticity observed in the stress response. We study the survival probability of the population and the population growth rate in constant and periodic environments. We evince a trade-off for population establishment, as well as a sensitivity with respect to the model parameters that differs for survival probability and growth rate.We conclude with an independent section, collaborative work initiated during CEMRACS 2022. We investigate numerically the spatial propagation of size-structured populations modeling the collective movement of Myxobacteria clusters via a system of reaction-diffusion equations
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Zhang, Jiheng. "Limited processor sharing queues and multi-server queues." Diss., Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/34825.

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We study two classes of stochastic systems, the limited processor sharing system and the multi-server system. They share the common feature that multiple jobs/customers are being processed simultaneously, which makes the study of them intrinsically difficult. In the limited processor sharing system, a limited number of jobs can equally share a single server, and the excess ones wait in a first-in-first-out buffer. The model is mainly motivated by computer related applications, such as database servers and packet transmission over the Internet. This model is studied in the first part of the thesis. The multi-server queue is mainly motivated by call centers, where each customer is handled by an agent. The number of customers being served at any time is limited by number of agents employed. Customers who can not be served upon arrival wait in a first-in-first-out buffer. This model is studied in the second part of the thesis.
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Pace, Michele. "Stochastic models and methods for multi-object tracking." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2011. http://tel.archives-ouvertes.fr/tel-00651396.

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La poursuite multi-cibles a pour objet le suivi d'un ensemble de cibles mobiles à partir de données obtenues séquentiellement. Ce problème est particulièrement complexe du fait du nombre inconnu et variable de cibles, de la présence de bruit de mesure, de fausses alarmes, d'incertitude de détection et d'incertitude dans l'association de données. Les filtres PHD (Probability Hypothesis Density) constituent une nouvelle gamme de filtres adaptés à cette problématique. Ces techniques se distinguent des méthodes classiques (MHT, JPDAF, particulaire) par la modélisation de l'ensemble des cibles comme un ensemble fini aléatoire et par l'utilisation des moments de sa densité de probabilité. Dans la première partie, on s'intéresse principalement à la problématique de l'application des filtres PHD pour le filtrage multi-cibles maritime et aérien dans des scénarios réalistes et à l'étude des propriétés numériques de ces algorithmes. Dans la seconde partie, nous nous intéressons à l'étude théorique des processus de branchement liés aux équations du filtrage multi-cibles avec l'analyse des propriétés de stabilité et le comportement en temps long des semi-groupes d'intensités de branchements spatiaux. Ensuite, nous analysons les propriétés de stabilité exponentielle d'une classe d'équations à valeurs mesures que l'on rencontre dans le filtrage non-linéaire multi-cibles. Cette analyse s'applique notamment aux méthodes de type Monte Carlo séquentielles et aux algorithmes particulaires dans le cadre des filtres de Bernoulli et des filtres PHD.
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Books on the topic "Measure-Valued stochastic processes"

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service), SpringerLink (Online, ed. Measure-Valued Branching Markov Processes. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2011.

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Jean-Pierre, Fouque, Hochberg Kenneth J, and Merzbach Ely, eds. Stochastic analysis: Random fields and measure-valued processes. Ramat-Gan, Israel: Gelbart Research Institute for Mathematical Sciences and the Emmy Noether Research Institute of Mathematics, Bar-Ilan University, 1996.

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1937-, Dawson Donald Andrew, and Université de Montréal. Centre de recherches mathématiques., eds. Measure-valued processes, stochastic partial differential equations, and interacting systems. Providence, R.I., USA: American Mathematical Society, 1994.

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Perkins, Edwin Arend. On the martingale problem for interactive measure-valued branching diffusions. Providence, R.I: American Mathematical Society, 1995.

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Measure-Valued Processes and Stochastic Flows. de Gruyter GmbH, Walter, 2023.

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Measure-Valued Processes and Stochastic Flows. de Gruyter GmbH, Walter, 2023.

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Measure-Valued Processes and Stochastic Flows. de Gruyter GmbH, Walter, 2023.

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Measure-Valued Branching Markov Processes. Springer Berlin / Heidelberg, 2023.

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Li, Zenghu. Measure-Valued Branching Markov Processes. Springer, 2011.

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Li, Zenghu. Measure-Valued Branching Markov Processes. Springer, 2012.

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Book chapters on the topic "Measure-Valued stochastic processes"

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Li, Zenghu. "Measure-Valued Branching Processes." In Probability Theory and Stochastic Modelling, 31–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 2022. http://dx.doi.org/10.1007/978-3-662-66910-5_2.

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Ethier, S. N., and R. C. Griffiths. "The Transition Function of a Measure-Valued Branching Diffusion with Immigration." In Stochastic Processes, 71–79. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4615-7909-0_9.

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Dawson, Donald. "Measure-valued processes Construction, qualitative behavior and stochastic geometry." In Stochastic Spatial Processes, 69–93. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0076239.

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Perkins, Edwin. "On the Continuity of Measure-Valued Processes." In Seminar on Stochastic Processes, 1990, 261–68. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4684-0562-0_13.

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Zhao, Xuelei. "On the Interacting Measure-Valued Branching Processes." In Stochastic Differential and Difference Equations, 345–53. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-1980-4_28.

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Fitzsimmons, P. J. "On the Martingale Problem for Measure-Valued Markov Branching Processes." In Seminar on Stochastic Processes, 1991, 39–51. Boston, MA: Birkhäuser Boston, 1992. http://dx.doi.org/10.1007/978-1-4612-0381-0_4.

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Hesse, Christian, and Armin Dunz. "Analysing Particle Sedimentation in Fluids by Measure-Valued Stochastic Processes." In Multifield Problems, 25–33. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-04015-7_3.

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Gorostiza, Luis G., and J. Alfredo López-Mimbela. "A Convergence Criterion for Measure-Valued Processes, and Application to Continuous Superprocesses." In Barcelona Seminar on Stochastic Analysis, 62–71. Basel: Birkhäuser Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-8555-3_4.

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Blath, Jochen. "Measure-valued Processes, Self-similarity and Flickering Random Measures." In Fractal Geometry and Stochastics IV, 175–96. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-0346-0030-9_6.

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"5 Stationary measure-valued processes." In Measure-valued Processes and Stochastic Flows, 121–50. De Gruyter, 2023. http://dx.doi.org/10.1515/9783110986518-005.

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Conference papers on the topic "Measure-Valued stochastic processes"

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Wang, Yan. "Simulating Drift-Diffusion Processes With Generalized Interval Probability." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70699.

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The Fokker-Planck equation is widely used to describe the time evolution of stochastic systems in drift-diffusion processes. Yet, it does not differentiate two types of uncertainties: aleatory uncertainty that is inherent randomness and epistemic uncertainty due to lack of perfect knowledge. In this paper, a generalized Fokker-Planck equation based on a new generalized interval probability theory is proposed to describe drift-diffusion processes under both uncertainties, where epistemic uncertainty is modeled by the generalized interval while the aleatory one is by the probability measure. A path integral approach is developed to numerically solve the generalized Fokker-Planck equation. The resulted interval-valued probability density functions rigorously bound the real-valued ones computed from the classical path integral method. The new approach is demonstrated by numerical examples.
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