Related papers: Drift Estimation for Stochastic Reaction-Diffusion…
Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…
This paper is concerned with analysis of coupled fractional reaction-diffusion equations. It provides analytical comparison for the fractional and regular reaction-diffusion systems. As an example, the reaction-diffusion model with cubic…
In this paper, we investigate stochastic heat equation with sublinear diffusion coefficients. By assuming certain concavity of the diffusion coefficient, we establish non-trivial moment upper bounds and almost sure spatial asymptotic…
In this paper, we prove some a priori estimates for a system of partial differential equations arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The unknowns of…
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…
We consider stochastic reaction-diffusion equations with colored noise and prove Schauder type estimates, which will depend on the color of the noise, for the stationary and evolution problems associated with the corresponding transition…
This paper presents a new parameter estimation method for It\^{o} diffusions such that the resulting model predicts the equilibrium statistics as well as the sensitivities of the underlying system to external disturbances. Our formulation…
We study the uniqueness of reaction-diffusion steady states in general domains with Dirichlet boundary data. Here we consider "positive" (monostable) reactions. We describe geometric conditions on the domain that ensure uniqueness and we…
We consider stochastic reaction-diffusion equations on a finite network represented by a finite graph. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given supplemented by a…
A non-parametric diffusion model with an additive fractional Brownian motion noise is considered in this work. The drift is a non-parametric function that will be estimated by two methods. On one hand, we propose a locally linear estimator…
We construct solutions of nonlinear reaction-diffusion equations with nonlinear boundary conditions in spaces where the problem is supercritical and show the nonlinear balance required between the nonlinear terms in order to obtain a…
Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…
This paper is a survey of recent contributions on estimation in stochastic differential equations with mixed-effects. These models involve N stochastic differential equations with common drift and diffusion functions but random parameters…
Steady state is an essential concept in reaction networks. Its stability reflects fundamental characteristics of several biological phenomena such as cellular signal transduction and gene expression. Because biochemical reactions occur at…
We consider the homogeneous stochastic differential equation with unknown parameter to be estimated. We prove that the standard maximum likelihood estimate is strongly consistent under very mild conditions. There are also established the…
In this paper we focus on the parameter estimation of dynamic load models with stochastic terms, in particular, load models where protection settings are uncertain, such as in aggregated air conditioning units. We show how the uncertainty…
In this paper, we study the estimation of drift and diffusion coefficients in a two dimensional system of N interacting particles modeled by a degenerate stochastic differential equation. We consider both complete and partial observation…
We consider semilinear evolution equations of the form $a(t)\partial_{tt}u + b(t) \partial_t u + Lu = f(x,u)$ and $b(t) \partial_t u + Lu = f(x,u),$ with possibly unbounded $a(t)$ and possibly sign-changing damping coefficient $b(t)$, and…
Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…
Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…