Non Stopping Times and Stopping Theorems
Ashkan Nikeghbali
Abstract
Given a random time, we characterize the set of martingales for which the stopping theorems still hold. We also investigate how the stopping theorems are modified when we consider arbitrary random times. To this end, we introduce some families of martingales with remarkable properties. We also investigate, in the Brownian setting, the relationships between a given random time and the underlying Brownian Motion in the progressively enlarged filtration with respect to this random time.
Create a lesson
Related papers
Sublinear multi-type preferential attachment
Anna Ben-Hamou, Nicolas Broutin, Camille Cazaux
Uniform Central Limit Theorems for Degree Distributions of Sparse Graphon Models
Robert Lunde, Soumendra Lahiri
Matching Random Point Sets with Minimum Distortion
Itai Benjamini, Mark Braverman, Elad Tzalik et al.
Uniqueness and full coverage in k-neighbor graphs
David Coupier, Benoît Henry, Benedikt Jahnel et al.
Bass martingales need not stretch
Mathias Beiglböck, Manuel Hasenbichler, Gudmund Pammer
Universality of smallest singular values of random row submatrices and phase retrieval problems
Shu Wen, Christian E. Häggblom, Xiufan Yang