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We study systems of reaction-diffusion equations perturbed by multiplicative noise, where the reaction terms satisfy quasipositivity, a triangular mass-control structure, and polynomial growth. Our results apply to a broad class of…

Probability · Mathematics 2026-05-27 Dionysis Milesis , Michael Salins

Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…

Analysis of PDEs · Mathematics 2010-03-12 Wei Wang , A. J. Roberts

Stochastic reaction networks is a powerful class of models for the representation a wide variety of population models including biochemistry. The control of such networks has been recently considered due to their important implications for…

Optimization and Control · Mathematics 2024-09-23 Corentin Briat , Mustafa Khammash

In order to understand the impact of random influences at physical boundary on the evolution of multiscale systems, a stochastic partial differential equation model under a fast random dynamical boundary condition is investigated. The…

Dynamical Systems · Mathematics 2008-08-07 Wei Wang , Jinqiao Duan

This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…

Probability · Mathematics 2014-02-11 Kai Liu

A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part.…

Statistics Theory · Mathematics 2020-02-26 Gregor Pasemann , Wilhelm Stannat

In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent…

Optimization and Control · Mathematics 2026-04-15 Akan Selim , Siddhartha Ganguly , Ali Pakniyat , Panagiotis Tsiotras

In this paper, we are concerned with the stochastic time-fractional diffusion-wave equations in a Hilbert space. The main objective of this paper is to establish properties of the stochastic weak solutions of the initial-boundary value…

Analysis of PDEs · Mathematics 2023-06-28 Matti Lassas , Zhiyuan Li , Zhidong Zhang

A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best…

Optimization and Control · Mathematics 2018-09-19 Eduardo Casas , Mariano Mateos , Fredi Tröltzsch

We consider a control problem constrained by the unsteady stochastic Stokes equations with nonhomogeneous boundary conditions in connected and bounded domains. In this paper, controls are defined inside the domain as well as on the…

Optimization and Control · Mathematics 2018-09-05 Peter Benner , Christoph Trautwein

We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…

Analysis of PDEs · Mathematics 2020-03-09 C. H. S. Hamster , H. J. Hupkes

A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear…

Traditional chemical kinetics may be inappropriate to describe chemical reactions in micro-domains involving only a small number of substrate and reactant molecules. Starting with the stochastic dynamics of the molecules, we derive a…

Mathematical Physics · Physics 2009-11-10 D. Holcman , Z. Schuss

We consider the control of semilinear stochastic partial differential equations (SPDEs) via deterministic controls. In the case of multiplicative noise, existence of optimal controls and necessary conditions for optimality are derived. In…

Optimization and Control · Mathematics 2021-10-28 Wilhelm Stannat , Lukas Wessels

This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena,…

Probability · Mathematics 2018-01-15 Pavel Mozgunov , Marco Beccuti , Andras Horvath , Thomas Jaki , Roberta Sirovich , Enrico Bibbona

In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a…

Probability · Mathematics 2016-12-05 Giuseppina Guatteri

In this paper, we study stochastic homogenization of a coupled diffusion-reaction system. The diffusion-reaction system is coupled to stochastic differential equations, which govern the changes in the media properties. Though homogenization…

Probability · Mathematics 2018-10-18 Hakima Bessaih , Yalchin Efendiev , Razvan Florian Maris

The classical models for irreversible diffusion-influenced reactions can be derived by introducing absorbing boundary conditions to over-damped continuous Brownian motion (BM) theory. As there is a clear corresponding stochastic process,…

Statistical Mechanics · Physics 2016-10-13 Mauricio J. Del Razo , Hong Qian

In this paper, we investigate the effects of stochastic resetting on diffusion in $\R^d\backslash \calU$, where $\calU$ is a bounded obstacle with a partially absorbing surface $\partial \calU$. We begin by considering a Robin boundary…

Statistical Mechanics · Physics 2022-06-29 Paul C. Bressloff

We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…

Optimization and Control · Mathematics 2018-03-12 Luis H. R. Alvarez E.