Related papers: Stochastic Processes Driven by Deterministic Scale…
We study a stochastic model of protein dynamics that explicitly includes delay in the degradation. We rigorously derive the master equation for the processes and solve it exactly. We show that the equations for the mean values obtained…
In this paper we study the dynamics of stochastic microorganism flocculation models. Given the strong influence of environmental and seasonal fluctuations that are present in these models, we propose a stochastic model that includes…
In this article we study a class of singular stochastic differential equations driven by fractional Brownian motion with Hurst parameter H<1/2. The solution is constructed as the limit of a family of approximating processes, and its…
The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients…
Since the introduction of Dyson's Brownian motion in early 1960's, there have been a lot of developments in the investigation of stochastic processes on the space of Hermitian matrices. Their properties, especially, the properties of their…
Dynamical systems techniques are a powerful tool to analyse systems of ordinary differential equations, written in an appropriate form. For a given theory of gravity, the cosmological field equations typically lead to a system of ordinary…
We study pathwise approximation of scalar stochastic differential equations at a single point. We provide the exact rate of convergence of the minimal errors that can be achieved by arbitrary numerical methods that are based (in a…
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…
In this paper we show that solutions of stochastic partial differential equations driven by Brownian motion can be approximated by stochastic partial differential equations forced by pure jump noise/random kicks. Applications to stochastic…
We consider a particle evolving in the quadratic potential and subject to a time-inhomogeneous frictional force and to a random force. The couple of its velocity and position is solution to a stochastic differential equation driven by an…
Motivated by the fact that in nature almost all phenomena behave randomly in some scales and deterministically in some other scales, we build up a framework suitable to tackle both deterministic and stochastic homogenization problems…
This paper presents a new stochastic finite element method for computing structural stochastic responses. The method provides a new expansion of stochastic response and decouples the stochastic response into a combination of a series of…
We formulate the large deviations for a class of two scale chemical kinetic processes motivated from biological applications. The result is successfully applied to treat a genetic switching model with positive feedbacks. The corresponding…
We present a general method for constructing stochastic processes with prescribed local form. Such processes include variable amplitude multifractional Brownian motion, multifractional $\alpha$-stable processes, and multistable processes,…
By using large deviation theory that deals with the decay of probabilities of rare events on an exponential scale, we study the longtime behaviors and establish action functionals for scaled Brownian motion and L\'evy processes with…
We present a class of stochastic processes in which the large deviation functions of time-integrated observables exhibit singularities that relate to dynamical phase transitions of trajectories. These illustrative examples include Brownian…
Optimization problems involving sequential decisions in a stochastic environment were studied in Stochastic Programming (SP), Stochastic Optimal Control (SOC) and Markov Decision Processes (MDP). In this paper we mainly concentrate on SP…
Many equations that model fluid behaviour are derived from systems that encompass multiple physical forces. When the equations are written in non dimensional form appropriate to the physics of the situation, the resulting partial…
The rate of strong convergence is investigated for an approximation scheme for a class of stochastic differential equations driven by a time-changed Brownian motion, where the random time changes $(E_t)_{t\ge 0}$ considered include the…
Mathematical models are vital interpretive and predictive tools used to assist in the understanding of cell migration. There are typically two approaches to modelling cell migration: either micro-scale, discrete or macro-scale, continuum.…