Related papers: General approximation method for the distribution …
Branching processes are a class of continuous-time Markov chains (CTMCs) prevalent for modeling stochastic population dynamics in ecology, biology, epidemiology, and many other fields. The transient or finite-time behavior of these systems…
We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…
The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…
We construct birth-and-death Markov evolution of states(distributions) of point particle systems in $\mathbb{R}^d$. In this evolution, particles reproduce themselves at distant points (disperse) and die under the influence of each other…
A common and effective method for calculating the steady-state distribution of a process under stochastic resetting is the renewal approach that requires only the knowledge of the reset-free propagator of the underlying process and the…
We consider a Markovian jumping process which is defined in terms of the jump-size distribution and the waiting-time distribution with a position-dependent frequency, in the diffusion limit. We assume the power-law form for the frequency.…
For a wide class of continuous-time Markov processes, including all irreducible hypoelliptic diffusions evolving on an open, connected subset of $\RL^d$, the following are shown to be equivalent: (i) The process satisfies (a slightly weaker…
We propose a systematic method to derive the asymptotic behaviour of the persistence distribution, for a large class of stochastic processes described by a general Fokker-Planck equation in one dimension. Theoretical predictions are…
We consider a system of $N$ particles interacting through their empirical distribution on a finite state space in continuous time. In the formal limit as $N\to\infty$, the system takes the form of a nonlinear (McKean--Vlasov) Markov chain.…
Markov chain Monte Carlo methods are central in computational statistics, and typically rely on detailed balance to ensure invariance with respect to a target distribution. Although straightforward to construct by Metropolization, this can…
We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the…
We present a simple and general framework to simulate statistically correct realizations of a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical an efficient algorithm alike the…
Spatial birth-and-death processes with time dependent rates are obtained as solutions to certain stochastic equations. The existence, uniqueness, uniqueness in law and the strong Markov property of unique solutions are proven when the…
We study a new technique for the asymptotic analysis of heavy-tailed systems conditioned on large deviations events. We illustrate our approach in the context of ruin events of multidimensional regularly varying random walks. Our approach…
We provide an original and general sufficient criterion ensuring the exponential contraction of Feynman-Kac semi-groups of penalized processes. This criterion is applied to time-inhomogeneous one-dimensional diffusion processes conditioned…
This paper provides full classification of dynamics for continuous time Markov chains (CTMCs) on the non-negative integers with polynomial transition rate functions. Such stochastic processes are abundant in applications, in particular in…
We study a McKean--Vlasov equation arising from a mean-field model of a particle system with positive feedback. As particles hit a barrier they cause the other particles to jump in the direction of the barrier and this feedback mechanism…
Filtering---estimating the state of a partially observable Markov process from a sequence of observations---is one of the most widely studied problems in control theory, AI, and computational statistics. Exact computation of the posterior…
We first prove a mimicking theorem (also known as a Markovian projection theorem) for the marginal distributions of an Ito process conditioned to not have exited a given domain. We then apply this new result to the proof of a conjecture of…
We consider the time evolution of the supercritical Galton-Watson model of branching particles with extra parameter (mass). In the moment of the division the mass of the particle (which is growing linearly after the birth) is divided in…