IDEAS home Printed from https://ideas.repec.org/p/aim/wpaimx/1616.html
   My bibliography  Save this paper

Infinite Dimensional Weak Dirichlet Processes and Convolution Type Processes

Author

Abstract

The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of weak Dirichlet process in this context. Such a process X, taking values in a Banach space H, is the sum of a local martingale and a suitableorthogonal process. The concept of weak Dirichlet process fits the notion of convolution type processes, a class including mild solutions for stochastic evolution equations on infinite dimensional Hilbert spaces and in particular of several classes of stochastic partial differential equations (SPDEs). In particular the mentioned decomposition appears to be a substitute of an Itô’s type formula applied to to f(t, X(t)) where f : [0, T ] × H ? R is a C0,1 function and X a convolution type processes.

Suggested Citation

  • Giorgio Fabbri & Francesco Russo, 2016. "Infinite Dimensional Weak Dirichlet Processes and Convolution Type Processes," AMSE Working Papers 1616, Aix-Marseille School of Economics, France, revised 20 Apr 2016.
    • Handle: RePEc:aim:wpaimx:1616
    as

    Download full text from publisher

    File URL: http://www.amse-aixmarseille.fr/sites/default/files/_dt/2012/wp_2016_-_nr_16.pdfFile-Format:Application/pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fabbri, Giorgio & Russo, Francesco, 2017. "Infinite dimensional weak Dirichlet processes and convolution type processes," Stochastic Processes and their Applications, Elsevier, vol. 127(1), pages 325-357.
    2. Cristina Girolami & Giorgio Fabbri & Francesco Russo, 2014. "The covariation for Banach space valued processes and applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(1), pages 51-104, January.
    3. Giorgio FABBRI & Francesco RUSSO, 2012. "Infinite dimensional weak Dirichlet processes, stochastic PDEs and optimal control," LIDAM Discussion Papers IRES 2012017, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    4. Gozzi, Fausto & Russo, Francesco, 2006. "Verification theorems for stochastic optimal control problems via a time dependent Fukushima-Dirichlet decomposition," Stochastic Processes and their Applications, Elsevier, vol. 116(11), pages 1530-1562, November.
    5. Errami, Mohammed & Russo, Francesco, 2003. "n-covariation, generalized Dirichlet processes and calculus with respect to finite cubic variation processes," Stochastic Processes and their Applications, Elsevier, vol. 104(2), pages 259-299, April.
    6. Gozzi, Fausto & Russo, Francesco, 2006. "Weak Dirichlet processes with a stochastic control perspective," Stochastic Processes and their Applications, Elsevier, vol. 116(11), pages 1563-1583, November.
    7. Editors The, 2007. "From the Editors," Basic Income Studies, De Gruyter, vol. 2(1), pages 1-5, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Giorgio Fabbri & Francesco Russo, 2017. "HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition," LIDAM Discussion Papers IRES 2017003, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    2. Giorgio Fabbri & Francesco Russo, 2016. "Infinite Dimensional Weak Dirichlet Processes and Convolution Type Processes," Working Papers halshs-01309384, HAL.
    3. Fabbri, Giorgio & Russo, Francesco, 2017. "Infinite dimensional weak Dirichlet processes and convolution type processes," Stochastic Processes and their Applications, Elsevier, vol. 127(1), pages 325-357.
    4. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fabbri, G. & Russo, F., 2017. "HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition," Working Papers 2017-07, Grenoble Applied Economics Laboratory (GAEL).
    2. Cristina Girolami & Giorgio Fabbri & Francesco Russo, 2014. "The covariation for Banach space valued processes and applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(1), pages 51-104, January.
    3. Giorgio Fabbri & Francesco Russo, 2016. "Infinite Dimensional Weak Dirichlet Processes and Convolution Type Processes," Working Papers halshs-01309384, HAL.
    4. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    5. Bandini, Elena & Russo, Francesco, 2017. "Weak Dirichlet processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 4139-4189.
    6. Bouchard, Bruno & Loeper, Grégoire & Tan, Xiaolu, 2022. "A ℂ0,1-functional Itô’s formula and its applications in mathematical finance," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 299-323.
    7. Michael R. CARTER & Alain de JANVRY & Elisabeth SADOULET & Alexandros SARRIS, 2014. "Index-based weather insurance for developing countries: A review of evidence and a set of propositions for up-scaling," Working Papers P111, FERDI.
    8. Elena Issoglio & Francesco Russo, 2024. "Stochastic Differential Equations with Singular Coefficients: The Martingale Problem View and the Stochastic Dynamics View," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2352-2393, September.
    9. Thiago Mastrangelo & Adalecio Kovaleski & Victor Botteon & Wanessa Scopel & Maria de Lourdes Zamboni Costa, 2018. "Optimization of the sterilizing doses and overflooding ratios for the South American fruit fly," PLOS ONE, Public Library of Science, vol. 13(7), pages 1-17, July.
    10. Eloi Laurent, 2010. "Environmental justice and environmental inequalities: A European perspective," SciencePo Working papers Main hal-01069412, HAL.
    11. Keith Finlay, 2009. "Effect of Employer Access to Criminal History Data on the Labor Market Outcomes of Ex-Offenders and Non-Offenders," NBER Chapters, in: Studies of Labor Market Intermediation, pages 89-125, National Bureau of Economic Research, Inc.
    12. Sylvester Ngome Chisika & Chunho Yeom, 2021. "Enhancing Sustainable Management of Public Natural Forests Through Public Private Partnerships in Kenya," SAGE Open, , vol. 11(4), pages 21582440211, October.
    13. Erling Barth & James C. Davis & Richard B. Freeman & Andrew J. Wang, 2018. "The Effects of Scientists and Engineers on Productivity and Earnings at the Establishment Where They Work," NBER Chapters, in: US Engineering in a Global Economy, pages 167-191, National Bureau of Economic Research, Inc.
    14. Laurent, Catherine E. & Berriet-Solliec, Marielle & Kirsch, Marc & Labarthe, Pierre & Trouve, Aurelie, 2010. "Multifunctionality Of Agriculture, Public Policies And Scientific Evidences: Some Critical Issues Of Contemporary Controversies," APSTRACT: Applied Studies in Agribusiness and Commerce, AGRIMBA, vol. 4(1-2), pages 1-6.
    15. Juan Carlos Conesa & Timothy J. Kehoe & Kim J. Ruhl, 2007. "Modeling great depressions: the depression in Finland in the 1990s," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 31(Nov), pages 16-44.
    16. Bruno Bouchard & Gr'egoire Loeper & Xiaolu Tan, 2021. "A $C^{0,1}$-functional It\^o's formula and its applications in mathematical finance," Papers 2101.03759, arXiv.org.
    17. Fabio Salamanca-Buentello & Mary V Seeman & Abdallah S Daar & Ross E G Upshur, 2020. "The ethical, social, and cultural dimensions of screening for mental health in children and adolescents of the developing world," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-25, August.
    18. Sherif Abdullahi & Amir Shaharuddin, 2016. "Potential for Islamic Banking in Macedonia: An Empirical Evidence," International Review of Management and Marketing, Econjournals, vol. 6(4), pages 1039-1047.
    19. Maćkowiak Henryk, 2011. "The Goods Structure of Trade between Polish Regions and the European Union (1)," Bulletin of Geography. Socio-economic Series, Sciendo, vol. 16(16), pages 57-74, January.
    20. Adilson Carlos Yoshikuni & José Eduardo Ricciardi Favaretto & Alberto Luiz Albertin & Fernando de Souza Meirelles, 2022. "How can Strategy-as-Practice Enable Innovation under the Influence of Environmental Dynamism?," RAC - Revista de Administração Contemporânea (Journal of Contemporary Administration), ANPAD - Associação Nacional de Pós-Graduação e Pesquisa em Administração, vol. 26(1), pages 200131-2001.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aim:wpaimx:1616. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Gregory Cornu (email available below). General contact details of provider: https://edirc.repec.org/data/amseafr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.