Related papers: Solving Poisson's Equation: Existence, Uniqueness,…
In this paper, we prove the existence and uniqueness of solutions as well as ergodicity for McKean-Vlasov SDEs under Lyapunov conditions, in which the Lyapunov functions are defined on $\mathbb R^d\times \mathcal P_2(\mathbb R^d)$, i.e. the…
In this paper, we establish novel concentration inequalities for additive functionals of geometrically ergodic Markov chains similar to Rosenthal inequalities for sums of independent random variables. We pay special attention to the…
Bertaut's equivalent electric density idea (E. F. Bertaut, Journal de Physique {\bf 39}, 1331 (1978)) is applied to the case of two dimensional periodic continuous charge density distributions. The following derivation differs from what was…
We overview results on the topic of Poisson approximation that are missed in existing surveys. The topic of Poisson approximation to the distribution of a sum of integer-valued random variables is presented as well. We do not restrict…
We investigate Maxwell-Chern-Simons theory on a three-dimensional noncommutative spacetime endowed with a constant spacelike Poisson structure. By exploiting the residual rotational symmetry, we construct exact classical solutions…
We establish new quantitative estimates for localized finite differences of solutions to the Poisson problem for the fractional Laplace operator with homogeneous Dirichlet conditions of solid type settled in bounded domains satisfying the…
In this paper, we study a class of multiscale McKean-Vlasov stochastic systems where the entire system depends on the distribution of the fast component. First of all, by the Poisson equation method we prove that the slow component…
We introduce a new minimisation principle for Poisson equation using two variables: the solution and the gradient of the solution. This principle allows us to use any conforming finite element spaces for both variables, where the finite…
This paper considers the problem of uniqueness of the solutions to a class of Markovian backward stochastic differential equations (BSDEs) which are also connected to certain nonlinear partial differential equation (PDE) through a…
The Poisson structure is constructed for a model in which spatial coordinates of configuration space are noncommutative and satisfy the commutation relations of a Lie algebra. The case is specialized to that of the group SU(2), for which…
We construct solutions to the randomly-forced Navier--Stokes--Poisson system in periodic three-dimensional domains or in the whole three-dimensional Euclidean space. These solutions are weak in the sense of PDEs and also weak in the sense…
Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems (including uniqueness, recurrence, ergodicity,…
In this paper, we develop some matrix Poisson's equations satisfied by the mean and variance of the mixing time in an irreducible positive-recurrent discrete-time Markov chain with infinitely-many levels, and provide a computational…
We consider a curved space-time whose algebra of functions is the commutative limit of a noncommutative algebra and which has therefore an induced Poisson structure. In a simple example we determine a relation between this structure and the…
We study the loop clusters induced by Poissonian ensembles of Markov loops on a finite or countable graph (Markov loops can be viewed as excursions of Markov chains with a random starting point, up to re-rooting). Poissonian ensembles are…
We consider a Markov chain on the space of (countable) partitions of the interval [0,1], obtained first by size biased sampling twice (allowing repetitions) and then merging the parts (if the sampled parts are distinct) or splitting the…
We prove the Simons-Johnson theorem for the sums $S_n$ of $m$-dependent random variables, with exponential weights and limiting compound Poisson distribution $\CP(s,\lambda)$. More precisely, we give sufficient conditions for…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…
The existence, uniqueness, and asymptotic stability of modulo periodic Poisson stable solutions of dynamic equations on a periodic time scale are investigated. The model under investigation involves a term which is constructed via a Poisson…