Related papers: Harmonic continuous-time branching moments

We study a class of statistical inverse problems with non-linear pointwise operators motivated by concrete statistical applications. A two-step procedure is proposed, where the first step smoothes the data and inverts the non-linearity.…

We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d \ge 3$ and the environment is "not too random", then, the total…

We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant population at some fixed time and prove…

We derive explicit representations for the (Siegmund) dual and the inverse flow of generalized Ornstein-Uhlenbeck processes whenever these exist. It turns out that the dual and the process corresponding to the inverse stochastic flow are…

Our principal aim is to observe the Markov discrete-time process of population growth with long-living trajectory. First we study asymptotical decay of generating function of Galton-Watson process for all cases as the Basic Lemma.…

We propose a class of non-Markov population models with continuous or discrete state space via a limiting procedure involving sequences of rescaled and randomly time-changed Galton--Watson processes. The class includes as specific cases the…

We consider a class of non-conjugate priors as a mixing family of distributions for a parameter (e.g., Poisson or gamma rate, inverse scale or precision of an inverse-gamma, inverse variance of a normal distribution) of an exponential…

We consider branching Brownian motion in which initially there is one particle at $x$, particles produce a random number of offspring with mean $m+1$ at the time of branching events, and each particle branches at rate $\beta = 1/2m$.…

In this paper, we propose new semiparametric procedures for making inference on linear functionals and their functions of two semicontinuous populations. The distribution of each population is usually characterized by a mixture of a…

Consider a discrete-time supercritical discounted branching random walk, in which increments at depth $k$ are independent and identically distributed with the same law as $m^{-kH}Y$, where $Y$ has a fixed law, $H>0$, and $m>1$ is the…

We consider shot noise processes $(X(t))_{t \geq 0}$ with deterministic response function $h$ and the shots occurring at the renewal epochs $0= S_0 < S_1 < S_2 ...$ of a zero-delayed renewal process. We prove convergence of the…

We consider a population with non-overlapping generations, whose size goes to infinity. It is described by a discrete genealogy which may be time non-homogeneous and we pay special attention to branching trees in varying environments. A…

We study the behavior of an infinite system of ordinary differential equations modeling the dynamics of a metapopulation, a set of (discrete) populations subject to local catastrophes and connected via migration under a mean field rule; the…

Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment assumptions. In this paper we present several…

It is well-known that compositions of Markov processes with inverse subordinators are governed by integro-differential equations of generalized fractional type. This kind of processes are of wide interest in statistical physics as they are…

Let $X_n(k)$ be the number of vertices at level $k$ in a random recursive tree with $n+1$ vertices. We are interested in the asymptotic behavior of $X_n(k)$ for intermediate levels $k=k_n$ satisfying $k_n\to\infty$ and $k_n=o(\log n)$ as…

In this work we investigate limit theorems for the time-averaged process $\left(\frac{1}{t}\int_0^t X_s^x ds\right)_{t\geq 0}$ where $X^x$ is a subcritical continuous-state branching processes with immigration (CBI processes) starting in $x…

Let $W_1,\ldots,W_N$ be a sample of $\mathrm{Pareto}(\alpha)$ random variables normalized by their sum, such that $\sum_i W_i=1$. The $W_i$ may represent the weights of valleys in a spin glass (if $0<\alpha<1$), or the frequency of…

We propose skewed stable random projections for approximating the pth frequency moments of dynamic data streams (0<p<=2), which has been frequently studied in theoretical computer science and database communities. Our method significantly…

First-passage properties are central to the kinetics of target-search processes. Theoretical approaches so far primarily focused on predicting first-passage statistics for a given process or model. In practice, however, one faces the…