Related papers: Duality for spatially interacting Fleming-Viot pro…
We uncover a duality between relaxation and first passage processes in ergodic reversible Markovian dynamics in both discrete and continuous state-space. The duality exists in the form of a spectral interlacing -- the respective time scales…
We consider a spatial multi-type branching model in which individuals migrate in geographic space according to random walks and reproduce according to a state-dependent branching mechanism which can be sub-, super- or critical depending on…
We develop criteria for recurrence and transience of one-dimensional Markov processes which have jumps and oscillate between $+\infty$ and $-\infty$. The conditions are based on a Markov chain which only consists of jumps (overshoots) of…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
The purpose of this paper is to investigate the long time behaviour for a self-interacting diffusion and a self-interacting velocity jump process. While the diffusion case has already been studied for some particular potential function, the…
We show, for a class of discrete Fleming-Viot (or Moran) type particle systems, that the convergence to the equilibrium is exponential for a suitable Wassertein coupling distance. The approach provides an explicit quantitative estimate on…
The large-deviation method can be used to study the measurement trajectories of open quantum systems. For optical arrangements this formalism allows to describe the long time properties of the (non-equilibrium) photon counting statistics in…
Different evolutionary models are known to make disparate predictions for the success of an invading mutant in some situations. For example, some evolutionary mechanics lead to amplification of selection in structured populations, while…
We consider the mutation--selection differential equation with pairwise interaction (or, equivalently, the diploid mutation--selection equation) and establish the corresponding ancestral process, which is a random tree and a variant of the…
Certain Markov processes, or deterministic evolution equations, have the property that they are dual to a stochastic process that exhibits extinction versus unbounded growth, i.e., the total mass in such a process either becomes zero, or…
We are interested in populations in which the fitness of different genetic types fluctuates in time and space, driven by temporal and spatial fluctuations in the environment. For simplicity, our population is assumed to be composed of just…
Motivated by questions of ergodicity for shift invariant Fleming-Viot process, we consider the centered Fleming-Viot process $\left(Z_{t} \right)_{t\geqslant 0}$ defined by $Z_{t} := \tau_{-\left\langle {\rm id}, Y_{t} \right\rangle} \sharp…
Let $(M,d,\mu)$ be a uniformly discrete metric measure space satisfying space homogeneous volume doubling condition. We consider discrete time Markov chains on $M$ symmetric with respect to $\mu$ and whose one-step transition density is…
We consider diffusion processes x_{t} on the unit interval. Doob-transformation techniques consist of a selection of x_{t}-paths procedure. The law of the transformed process is the one of a branching diffusion system of particles, each…
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
An idea for evaluating transition probabilities in chemical reaction systems is proposed, which is efficient for repeated calculations with various rate constants. The idea is based on duality relations; instead of direct time-evolutions of…
We consider a Fleming-Viot-type particle system consisting of independently moving particles that are killed on the boundary of a domain. At the time of death of a particle, another particle branches. If there are only two particles and the…
We investigate the two-points correlation function for several boundary-driven interacting particle systems. Our goal is to show that the time evolution of that correlation function is solution to a partial differential equation that can be…
We study the evolution of genealogies of a population of individuals, whose type frequencies result in an interacting Fleming-Viot process on $\Z$. We construct and analyze the genealogical structure of the population in this…
We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves…