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Semimartingales on Duals of Nuclear Spaces
- Source :
- Electron. J. Probab., Electronic Journal of Probability, Volume 25, paper no. 36 (2020), Kérwá, Universidad de Costa Rica, instacron:UCR
- Publication Year :
- 2019
- Publisher :
- arXiv, 2019.
-
Abstract
- This work is devoted to the study of semimartingales on the dual of a general nuclear space. We start by establishing conditions for a cylindrical semimartingale in the strong dual Φ′ of a nuclear space Φ to have a Φ′-valued semimartingale version whose paths are right-continuous with left limits. Results of similar nature but for more specific classes of cylindrical semimartingales and examples are also provided. Later, we will show that under some general conditions every semimartingale taking values in the dual of a nuclear space has a canonical representation. The concept of predictable characteristics is introduced and is used to establish necessary and sufficient conditions for a Φ′-valued semimartingale to be a Φ′-valued Lévy process. UCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias Básicas::Centro de Investigaciones en Matemáticas Puras y Aplicadas (CIMPA) UCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de Matemática
- Subjects :
- Statistics and Probability
Pure mathematics
Statistics::Theory
60B11
regularization theorem
Nuclear space
Mathematics::Optimization and Control
Lévy process
Proceso estocástico
Mathematics::Probability
semimartingales
60G48
FOS: Mathematics
Canonical form
60G20
Mathematics
Teoría de la probabilidad
dual of a nuclear space
Probability (math.PR)
cylindrical semimartingales
60B11, 60G17, 60G20, 60G48
semimartingale canonical representation
Dual (category theory)
Semimartingale
Lévy processes
60G17
Dual polyhedron
Statistics, Probability and Uncertainty
Mathematics - Probability
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Electron. J. Probab., Electronic Journal of Probability, Volume 25, paper no. 36 (2020), Kérwá, Universidad de Costa Rica, instacron:UCR
- Accession number :
- edsair.doi.dedup.....ce5c295aa6c302a0f0c3e0efc9fd76c5
- Full Text :
- https://doi.org/10.48550/arxiv.1902.03981