Related papers: Exact solution of a stochastic protein dynamics mo…

In this note, we shall consider the existence of invariant measures for a class of infinite dimensional stochastic functional differential equations with delay whose driving semigroup is eventually norm continuous. The results obtained are…

We consider multistage stochastic linear optimization problems combining joint dynamic probabilistic constraints with hard constraints. We develop a method for projecting decision rules onto hard constraints of wait-and-see type. We…

We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…

In this paper, we proved moderate deviation principles for a fully coupled two-time-scale stochastic systems, where the slow process is given by stochastic differential equations with small noise, while the fast process is a rapidly…

Background: Many attempts have been made to resolve in time the folding of model proteins in computer simulations. Different computational approaches have emerged. Some of these approaches suffer from the insensitivity to the geometrical…

We describe a general scheme of derivation of the Vlasov-type equations for Markov evolutions of particle systems in continuum. This scheme is based on a proper scaling of corresponding Markov generators and has an algorithmic realization…

We study the existence and uniqueness of a solution for the multivalued stochastic differential equation with delay (the multivalued term is of subdifferential type): \[ \left\{\begin{array} [c]{r} dX(t)+\partial\varphi\left(X(t)\right)…

The stochastic protein kinetic equations can be stiff for certain parameters, which makes their numerical simulation rely on very small time step sizes, resulting in large computational cost and accumulated round-off errors. For such…

Delays are ubiquitous in applied problems, but often do not arise as the simple constant discrete delays that analysts and numerical analysts like to treat. In this chapter we show how state-dependent delays arise naturally when modeling…

Genetic feedback loops in cells break detailed balance and involve bimolecular reactions; hence exact solutions revealing the nature of the stochastic fluctuations in these loops are lacking. We here consider the master equation for a gene…

We propose two dynamical models with delay taking advantage of their complex dynamics for information processing tasks. The first model incorporates coupled delayed dynamics of multiple bits, which is shown to have desirable properties as…

By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of differential equations with…

The phenomena of stochasticity in biochemical processes have been intriguing life scientists for the past few decades. We now know that living cells take advantage of stochasticity in some cases and counteract stochastic effects in others.…

This paper focuses on the dynamical properties of delayed complex balanced systems. We first study the relationship between the stoichiometric compatibility classes of delayed and non-delayed systems. Using this relation we give another way…

In performative prediction, the choice of a model influences the distribution of future data, typically through actions taken based on the model's predictions. We initiate the study of stochastic optimization for performative prediction.…

Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…

In this paper, we consider a class of multi-dimensional stochastic delay differential equations with jump reflection. Based on existence and uniqueness of the strong solution to the equation, we prove that the Markov semigroup generated by…

It is a well established result that, in classical dynamical systems with sufficient time-scale separation, the fast chaotic degrees of freedom are well modeled by (Gaussian) white noise. In this paper, we present the stochastic dynamical…

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations, hence there is considerable interest…

Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a…