Related papers: Survival probabilities of autoregressive processes
In many Phase II statistical process control (SPC) problems, the main concern is not whether a monitored process has ever changed, but whether it is currently operating at an acceptable level. This distinction is especially important when…
We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We…
We consider survival probabilities for the discrete time process in one dimension, which is known as the Domany-Kinzel model. A convergence theorem for infinite systems can be obtained in the nonattractive case.
While there are many well-known and extensively tested results involving diffusion-limited binary reactions, reactions involving subdiffusive reactant species are far less understood. Subdiffusive motion is characterized by a mean square…
An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models are useful for…
In this paper, we prove almost surely consistency of a Survival Analysis model, which puts a Gaussian process, mapped to the unit interval, as a prior on the so-called hazard function. We assume our data is given by survival lifetimes $T$…
This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong…
Let X be some homogeneous additive functional of a skew Bessel process Y. In this note, we compute the asymptotics of the first passage time of X to some fixed level b, and study the position of Y when X exits a bounded interval [a, b]. As…
An inhomogeneous first--order integer--valued autoregressive (INAR(1)) process is investigated, where the autoregressive type coefficient slowly converges to one. It is shown that the process converges weakly to a Poisson or a compound…
We extend classical results about the convergence of nearly unstable AR(p) processes to the infinite order case. To do so, we proceed as in recent works about Hawkes processes by using limit theorems for some well chosen geometric sums. We…
Convergence results for averages of independent replications of counting processes are established in a $p$-variation setting and under certain assumptions. Such convergence results can be combined with functional differentiability results…
In this paper, we obtain an asymptotic formula for the persistence probability in the positive real line of a random polynomial arising from evolutionary game theory. It corresponds to the probability that a multi-player two-strategy random…
In this paper we first provide several conditional limit theorems for L\'evy processes with negative drift and regularly varying tail. Then we apply them to study the asymptotic behavior of expectations of some exponential functionals of…
Large language and music models are increasingly used for constrained generation: rhyming lines, fixed meter, inpainting or infilling, positional endings, and other global form requirements. These systems often perform strikingly well, but…
We describe an algorithm that takes as input a complex sequence $(u_n)$ given by a linear recurrence relation with polynomial coefficients along with initial values, and outputs a simple explicit upper bound $(v_n)$ such that $|u_n| \leq…
We explore the concept of a consistent exchangeable survival process - a joint distribution of survival times in which the risk set evolves as a continuous-time Markov process with homogeneous transition rates. We show a correspondence with…
We study the asymptotic tail behaviour of the first-passage time over a moving boundary for asymptotically $\alpha$-stable L\'evy processes with $\alpha<1$. Our main result states that if the left tail of the L\'evy measure is regularly…
We study the probability that an AR(1) Markov chain $X_{n+1}=aX_n+\xi_{n+1}$, where $a\in(0,1)$ is a constant, stays non-negative for a long time. We find the exact asymptotics of this probability and the weak limit of $X_n$ conditioned to…
We consider a supercritical branching random walk in time-inhomogeneous random environment with a random absorption barrier, i.e.,in each generation, only the individuals born below the barrier can survive and reproduce. Assume that the…
Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a renewal process. One ruin problem…