Related papers: Stochastic reaction-diffusion equations on network…
This work focuses on the well-posedness of abstract stochastic linear systems with boundary input delay and unbounded observation operators. We use product spaces and a semigroup approach to reformulate such delay systems into free-delay…
We obtain a probabilistic solution to linear-quadratic optimal control problems with state constraints. Given a closed set $\mathcal{D}\subseteq [0,T]\times\mathbb{R}^d$, a diffusion $X$ in $\mathbb{R}^d$ must be linearly controlled in…
The paper deals with non-linear Poisson neuron network models with bounded memory dynamics, that can include both Hebbian learning mechanisms and refractory periods. The state of a network is described by the times elapsed since its neurons…
Schr\"{o}dinger bridge can be viewed as a continuous-time stochastic control problem where the goal is to find an optimally controlled diffusion process whose terminal distribution coincides with a pre-specified target distribution. We…
The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as for instance the fluctuations in ribsome copy numbers for a gene regulatory network. While several…
Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which a linear path functional of the…
The use of fully or partially absorbing boundary conditions for diffusion-based problems has become paradigmatic in physical chemistry and biochemistry to describe reactions occurring in solutions or in living media. However, as chemical…
We consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two…
In this paper, we explore the solvability and the optimal control problem for a compartmental model based on reaction-diffusion partial differential equations describing a transmissible disease. The nonlinear model takes into account the…
We consider a system of nonlinear partial differential equations with stochastic dynamical boundary conditions that arises in models of neurophysiology for the diffusion of electrical potentials through a finite network of neurons.…
We address the question: Why may reaction-diffusion equations with hysteretic nonlinearities become ill-posed and how to amend this? To do so, we discretize the spatial variable and obtain a lattice dynamical system with a hysteretic…
We consider strong convergence of the finite differences approximation in space for stochastic reaction diffusion equations with multiplicative noise under a one-sided Lipschitz condition only. We derive convergence with an implicit rate…
Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…
This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation. We demonstrate that the existence of the time-scale separation naturally leads to the application of the averaging principle and…
Reflected diffusions naturally arise in many problems from applications ranging from economics and mathematical biology to queueing theory. In this paper we consider a class of infinite time-horizon singular stochastic control problems for…
This paper addresses a distributed optimization problem in a communication network where nodes are active sporadically. Each active node applies some learning method to control its action to maximize the global utility function, which is…
Stochastic reaction networks, which are usually modeled as continuous-time Markov chains on $\mathbb Z^d_{\ge 0}$, and simulated via a version of the "Gillespie algorithm," have proven to be a useful tool for the understanding of processes,…
The problem of estimating the reaction coefficient of a system governed by a reaction-diffusion partial differential equation is tackled. An estimator relying on boundary measurements only is proposed. The estimator is based upon a setpoint…