Related papers: Ratio limit theorem for renewal processes

We study the long time behaviour of a Markov process evolving in $\mathbb{N}$ and conditioned not to hit 0. Assuming that the process comes back quickly from infinity, we prove that the process admits a unique quasi-stationary distribution…

Optimal reinsurance when Value at Risk and expected surplus is balanced through their ratio is studied, and it is demonstrated how results for risk-adjusted surplus can be utilized. Simplifications for large portfolios are derived, and this…

We consider contact processes on the hierarchical group, where sites infect other sites at a rate depending on their hierarchical distance, and sites become healthy with a constant recovery rate. If the infection rates decay too fast as a…

Let $X$ be a continuous-time strongly mixing or weakly dependent process and $T$ a renewal process independent of $X$ with inter-arrival times $\tau$. We show general conditions under which the sampled process $(X_{T_i},T_i-T_{i-1})^{\top}$…

In this paper, we consider a risk process with deterministic growth and multiplicative jumps to model the capital of a low-income household. Reflecting the high-risk nature of the low-income environment, capital losses are assumed to be…

This paper considers an opportunistic scheduling problem over a renewal system. A controller observes a random event at the beginning of each renewal frame and then chooses an action in response to the event, which affects the duration of…

Let $\{X_{k,i};i\geq 1,k\geq 1\}$ be an array of i.i.d. random variables and let $\{p_n;n\geq 1\}$ be a sequence of positive integers such that $n/p_n$ is bounded away from 0 and $\infty$. For $W_n=\max_{1\leq i<j\leq…

Motivated by applications to COVID dynamics, we describe a branching process in random environments model $\{Z_n\}$ whose characteristics change when crossing upper and lower thresholds. This introduces a cyclical path behavior involving…

In this paper we give few expressions and asymptotics of ruin probabilities for a Markov modulated risk process for various regimes of a time horizon, initial reserves and a claim size distribution. We also consider few versions of the ruin…

We establish that if a sequence of spaces equipped with resistance metrics and measures converge with respect to the Gromov-Hausdorff-vague topology, and a certain non-explosion condition is satisfied, then the associated stochastic…

The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…

Strong ratio limit theorems associated with a broad class of spread out random walks on unimodular groups were proved in the preceding paper, where these random walks were assumed to have the convergence parameter $R=1$. In the present…

This paper presents comparison results and establishes risk bounds for credit portfolios within classes of Bernoulli mixture models, assuming conditionally independent defaults that are stochastically increasing with a common risk factor.…

We present some exact results for branching and annihilating random walks. We compute the nonuniversal threshold value of the annihilation rate for having a phase transition in the simplest reaction-diffusion system belonging to the…

We provide necessary and sufficient conditions for explosion and implosion of birth-and-death (non-Markov) continuous-time random walks. In other words, we obtain conditions for $\infty$ to be accessible and for it to be an entrance point.…

Consider an nxn random matrix X with i.i.d. nonnegative entries with bounded density, mean m, and finite positive variance sigma^2. Let M be the nxn random Markov matrix with i.i.d. rows obtained from X by dividing each row of X by its sum.…

By a random process with immigration at random times we mean a shot noise process with a random response function (response process) in which shots occur at arbitrary random times. The so defined random processes generalize random processes…

Renewal processes are broadly used to model stochastic behavior consisting of isolated events separated by periods of quiescence, whose durations are specified by a given probability law. Here, we identify the minimal sufficient statistic…

We consider the continuum limit of some products of random matrices in $\text{SL}(d,{\mathbb R})$ that arise as discretisations of incompressible renewing flows -- that is, of flows corresponding to a divergence-free velocity field that…

Let $\{X, X_n, n\geq 1\}$ be a sequence of independent identically distributed non-degenerate random variables. Put $S_0=0, S_n = \sum^n_{i=1} X_i$ and $V_n^2=\sum^n_{i=1} X_i^2, n\ge 1.$ A weak convergence theorem is established for the…