Related papers: Spatial birth and death processes as solutions of …
In this paper, we introduce concepts of pathwise random almost periodic and almost automorphic solutions for dynamical systems generated by non-autonomous stochastic equations. These solutions are pathwise stochastic analogues of…
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence, uniqueness and path-continuity of infinite-time solutions is proved by an extension of the Ovsyannikov method. This…
A probabilistic approach of computing geometric rate of convergence of stochastic processes is introduced in this paper. The goal is to quantitatively compute both upper and lower bounds of the exponential rate of convergence to the…
Equilibrium states in galactic dynamics can be described as stationary solutions of the Vlasov-Poisson system, which is the non-relativistic case, or of the Vlasov-Einstein system, which is the relativistic case. To obtain spherically…
To study later spatial evolutionary games based on the multitype contact process, we first focus in this paper on the conditions for survival/extinction in the presence of only one strategy, in which case our model consists of a variant of…
The construction of stochastic solutions is a powerful method to obtain localized solutions in configuration or Fourier space and for parallel computation with domain decomposition. Here a stochastic solution is obtained for the…
We consider optimal control of a new type of non-local stochastic partial differential equations (SPDEs). The SPDEs have space interactions, in the sense that the dynamics of the system at time $t$ and position in space x also depend on the…
In this work we address the analysis of discrete-time models of structured metapopulations subject to environmental stochasticity. Previous works on these models made use of the fact that migrations between the patches can be considered…
We study a class of multi-species birth-and-death processes going almost surely to extinction and admitting a unique quasi-stationary distribution (qsd for short). When rescaled by $K$ and in the limit $K\to+\infty$, the realizations of…
In this paper analogically as quadratic stochastic operators and processes we define cubic stochastic operator (CSO) and cubic stochastic processes (CSP). These are defined on the set of all probability measures of a measurable space. The…
For a birth-death process subject to catastrophes, defined on the state-space $S=\{r,r+1,r+2,...\}$, with $r$ a positive integer or zero, the first-visit time to a state $k\in S$ is considered and the Laplace transform of its probability…
The paper considers a particular family of set--valued stochastic processes modeling birth--and--growth processes. The proposed setting allows us to investigate the nucleation and the growth processes. A decomposition theorem is established…
We develop a McKean-Vlasov interpretation of Navier-Stokes equations with external force field in the whole space, by associating with local mild $L^p$-solutions of the 3d-vortex equation a generalized nonlinear diffusion with random…
A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…
The birth-death process is a special type of continuous-time Markov chain with index set $\mathbb{N}$. Its resolvent matrix can be fully characterized by a set of parameters $(\gamma, \beta, \nu)$, where $\gamma$ and $\beta$ are…
We analyze an interacting particle system with a Markov evolution of birth-and-death type. We have shown that a local competition mechanism (realized via a density dependent mortality) leads to a globally regular behavior of the population…
The normalised partial sums of values of a nonnegative multiplicative function over divisors with appropriately restricted sizes of a random permutation from the symmetric group define trajectories of a stochastic process. We prove a…
We perform a qualitative and thermodynamic study of two models when one takes into account adiabatic particle production. In the first one, there is a constant particle production rate, which leads to solutions depicting the current cosmic…
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system…
In this article, we consider time-changed models of population evolution $\mathcal{X}^f(t)=\mathcal{X}(H^f(t))$, where $\mathcal{X}$ is a counting process and $H^f$ is a subordinator with Laplace exponent $f$. In the case $\mathcal{X}$ is a…