Related papers: Stopping Times Occurring Simultaneously
Given a stochastic structure with a filtration $\mathbb{F}$, the class of all random times whose conditional distribution functions are differentiable with respect to some $\mathbb{F}$ adapted non decreasing processes is considered. The…
In this short paper, we connect the procedure of constructing a totally inaccessible stopping time for a given process using the well-known Cox construction, dependent on an independent exponential random variable; with naturally occurring…
Let $T\$ be a stopping time associated with a sequence of independent random variables $Z_{1},Z_{2},...$ . By applying a suitable change in the probability measure we present relations between the moment or probability generating functions…
Properties of arrival times are studied for a Cox process with independent (and stationary) increments. Under a reasonable setting the directing random measure is shown to take over independent (and stationary) increments of the process,…
A time-varying bivariate copula joint model, which models the repeatedly measured longitudinal outcome at each time point and the survival data jointly by both the random effects and time-varying bivariate copulas, is proposed in this…
We propose a novel approach to estimate the Cox model with temporal covariates. Our new approach treats the temporal covariates as arising from a longitudinal process which is modeled jointly with the event time. Different from the…
In this paper, we considered the problem of dependent censoring models with a positive probability that the times of failure are equal. In this context, we proposed to consider the Marshall-Olkin type model and studied some properties of…
Three notions of random stopping times exist in the literature. We introduce two concepts of equivalence of random stopping times, motivated by optimal stopping problems and stopping games respectively. We prove that these two concepts…
Longitudinal and survival sub-models are two building blocks for joint modelling of longitudinal and time to event data. Extensive research indicates separate analysis of these two processes could result in biased outputs due to their…
The relationship between a time-dependent covariate and survival times is usually evaluated via the Cox model. Time-dependent covariates are generally available as longitudinal data collected regularly during the course of the study. A…
Let $X_1,X_2,\ldots $ be independent random variables observed sequentially and such that $X_1,\ldots,X_{\theta-1}$ have a common probability density $p_0$, while $X_\theta,X_{\theta+1},\ldots $ are all distributed according to $p_1\neq…
This paper is concerned with modeling the dependence structure of two (or more) time-series in the presence of a (possible multivariate) covariate which may include past values of the time series. We assume that the covariate influences…
From the perspective of expectations of randomly stopped sums, Wald's equation and the Optional Sampling Theorem identify situations in which the stopping time can be decoupled from the stopping place, acting as if the two were independent.…
Study of recurrences in earthquakes, climate, financial time-series, etc. is crucial to better forecast disasters and limit their consequences. However, almost all the previous phenomenological studies involved only a long-ranged…
This paper deals with dependence across marginally exponentially distributed arrival times, such as default times in financial modeling or inter-failure times in reliability theory. We explore the relationship between dependence and the…
In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel…
A central focus in survival analysis is examining how covariates influence survival time. These covariate effects are often found to be either time-varying, heterogeneous - such as being specific to patients, treatments, or subgroups - or…
In statistics, time-to-event analysis methods traditionally focus on the estimation of hazards. In recent years, machine learning methods have been proposed to directly predict the event times. We propose a method based on vine copula…
We propose a multivariate framework for modeling dependent default times that extends the classical Cox process by incorporating both common and idiosyncratic shocks. Our construction uses c\`adl\`ag, increasing processes to model…
There exists a simple, didactically useful one-to-one relationship between stopping times and adapted c\`agl\`ad (LCRL) processes that are non-increasing and take the values 0 and 1 only. As a consequence, stopping times are always hitting…