15 citations · 20 across the 11 of their papers we have counts for
7 papers · 2 filters
An essay on the general theory of stochastic processes
Ashkan Nikeghbali
This text is a survey of the general theory of stochastic processes, with a view towards random times and enlargements of filtrations. The first five chapters present standard mate…
Multiplicative decompositions and frequency of vanishing of nonnegative submartingales
Ashkan Nikeghbali
In this paper, we establish a multiplicative decomposition formula for nonnegative local martingales and use it to characterize the set of continuous local submartingales Y of the…
How badly are the Burholder-Davis-Gundy inequalities affected by arbitrary random times?
Ashkan Nikeghbali
This note deals with the question: what remains of the Burkholder-Davis-Gundy inequalities when stopping times are replaced by arbitrary random times ? We prove that these i…
Enlargements of filtrations and path decompositions at non-stopping times
Ashkan Nikeghbali
Azéma associated with an honest time L the supermartingale and established some of its important properties. This supermartingale plays…
A class of remarkable submartingales
Ashkan Nikeghbali
In this paper, we consider the special class of positive local submartingales (X_{t}) of the form: X_{t}=N_{t}+A_{t}, where the measure (dA_{t}) is carried by the set {t: X_{t}=0}.…
Non Stopping Times and Stopping Theorems
Ashkan Nikeghbali
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…