Stochastic Integration With Respect to Cylindrical Semimartingales

 

Guardado en:
书目详细资料
作者: Fonseca Mora, Christian Andrés
格式: artículo original
Fecha de Publicación:2021
实物特征:In this work we introduce a theory of stochastic integration with respect to general cylindrical semimartingales defined on a locally convex space Φ. Our construction of the stochastic integral is based on the theory of tensor products of topological vector spaces and the property of good integrators of real-valued semimartingales. This theory is further developed in the case where Φ is a complete, barrelled, nuclear space, where we obtain a complete description of the class of integrands as Φ-valued locally bounded and weakly predictable processes. Several other properties of the stochastic integral are proven, including a Riemann representation, a stochastic integration by parts formula and a stochastic Fubini theorem. Our theory is then applied to provide sufficient and necessary conditions for existence and uniqueness of solutions to linear stochastic evolution equations driven by semimartingale noise taking values in the strong dual Φ′ of Φ. In the last part of this article we apply our theory to define stochastic integrals with respect to a sequence of real-valued semimartingales.
País:Kérwá
机构:Universidad de Costa Rica
Repositorio:Kérwá
语言:Inglés
OAI Identifier:oai:kerwa.ucr.ac.cr:10669/86887
在线阅读:https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Stochastic-integration-with-respect-to-cylindrical-semimartingales/10.1214/21-EJP718.full
https://hdl.handle.net/10669/86887
Palabra clave:Cylindrical semimartingales
locally convex spaces
NUCLEAR PHYSICS
stochastic integrals
tensor products