Related papers: Parameter Estimation in Two-type Continuous-state …
For an affine two factor model, we study the asymptotic properties of the maximum likelihood and least squares estimators of some appearing parameters in the so-called subcritical (ergodic) case based on continuous time observations. We…
The explicit criteria for several types of ergodicity of one-dimensional diffusions or birth-death processes have been found out recently in a surprisingly short period. One of the criteria is for exponential ergodicity of birth-death…
Let $\{Y_{n}$, $n \geq 1\}$ be a critical branching process with immigration having finite variance for the offspring number of particles and finite mean for the immigrating number of particles. In this paper, we study lower deviation…
We observe the Galton-Watson Branching Processes. Limit properties of transition functions and their convergence to invariant measures are investigated.
In this paper, we use a linear birth and death process with immigration to model infectious disease propagation when contamination stems from both person-to-person contact and contact with the environment. Our aim is to estimate the…
We introduce a class of one-dimensional positive Markov processes generalizing continuous-state branching processes (CBs), by taking into account a phenomenon of random collisions. Besides branching, characterized by a general mechanism…
Two types of random evolution processes are studied for ensembles of the standard map with driving parameter $K$ that determines its degree of stochasticity. For one type of processes the parameter $K$ is chosen at random from a Gaussian…
Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely…
We consider the problem of estimating the parameters of a supercritical controlled branching process consistently from a single observed trajectory of population size counts. Our goal is to establish which parameters can and cannot be…
We first introduce and derive some basic properties of a two-parameters family of one-sided Levy processes. Their Laplace exponents are given in terms of the Pochhammer symbol. This family includes, in a limit case, the family of Brownian…
We establish the joint scaling limit of a critical Bienaym\'e-Galton-Watson process with immigration (BGWI) and its (counting) local time at zero to the corresponding self-similar continuous-state branching process with immigration (CBI)…
This paper is concerned with combined inference for point processes on the real line observed in a broken interval. For such processes, the classic history-based approach cannot be used. Instead, we adapt tools from sequential spatial point…
By using the coupling technique, we present sufficient conditions for the exponential ergodicity of general continuous-state nonlinear branching processes in both the $L^1$-Wasserstein distance and the total variation norm, where the drift…
Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the…
In this article we focus on the partial sum $S_{n}=X_{1}+\cdots+X_{n}$ of the subcritical branching process with immigration $\{X_{n}\}_{n\in\mathbb{N_{+}}}$, under the condition that one of the offspring $\xi$ or immigration $\eta$ is…
In the present paper, we characterize the behavior of supercritical branching processes in random environment with linear fractional offspring distributions, conditioned on having small, but positive values at some large generation. As it…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
When particles/molecules diffuse in systems that contain obstacles, the steady-state regime (during which the mean-square displacement scales linearly with time, $\left< r^2 \right> \sim t$) is preceded by a transient regime. It is common…
We study ergodic properties of a class of Markov-modulated general birth-death processes under fast regime switching. The first set of results concerns the ergodic properties of the properly scaled joint Markov process with a parameter that…
This paper first strictly proved that the growth of the second moment of a large class of Gaussian processes is not greater than power function and the covariance matrix is strictly positive definite. Under these two conditions, the maximum…