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This paper is concerned with solutions to a one dimensional linear diffusion equation and their relation to some problems in stochastic control theory. A stochastic variational formula is obtained for the logarithm of the solution to the…

Optimization and Control · Mathematics 2009-12-02 Joseph G. Conlon , Mohar Guha

Stochastic modeling of chemical reaction systems based on master equations has been an indispensable tool in physical sciences. In the long-time limit, the properties of these systems are characterized by stationary distributions of…

Statistical Mechanics · Physics 2023-05-03 Yuji Hirono , Ryo Hanai

We study stationary distributions in the context of stochastic reaction networks. In particular, we are interested in complex balanced reaction networks and reduction of such networks by assuming a set of species (called non-interacting…

Probability · Mathematics 2024-02-06 Linard Hoessly , Carsten Wiuf , Panqiu Xia

We derive a stochastic partial differential equation that describes the fluctuating behaviour of reaction-diffusion systems of N particles, undergoing Markovian, unary reactions. This generalises the work of Dean [J. Phys. A: Math. and…

Statistical Mechanics · Physics 2025-01-13 Richard E. Spinney , Richard G. Morris

Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…

Optimization and Control · Mathematics 2020-12-15 Dmitriy Drusvyatskiy , Lin Xiao

We consider a diffusion problem on a network on whose nodes we impose Dirichlet and generalized, non-local Kirchhoff-type conditions. We prove well-posedness of the associated initial value problem, and we exploit the theory of…

Analysis of PDEs · Mathematics 2018-12-21 Delio Mugnolo

In this paper, we consider optimal control problems derived by stochastic systems with delay, where control domains are non-convex and the diffusion coefficients depend on control variables. By an estimate of the integral of…

Optimization and Control · Mathematics 2022-10-25 Qixia Zhang

Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor…

Probability · Mathematics 2022-02-28 Daniele Cappelletti , Badal Joshi

We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…

Optimization and Control · Mathematics 2017-07-07 Erhan Bayraktar , Christopher W. Miller

In this paper a stochastic reaction diffusion system is considered, which models the spread of a finite population reacting with a non-renewable resource in the presence of individual based noise. A two-parameter phase diagram is…

Probability · Mathematics 2009-01-27 Carl Mueller , Roger Tribe

This work studies the instability of stochastic scalar reaction diffusion equations, driven by a multiplicative noise that is white in time and smooth in space, near to zero, which is assumed to be a fixed point for the equation. We prove…

Probability · Mathematics 2024-06-10 Alexandra Blessing , Tommaso Rosati

We study reinforcement learning for controlled diffusion processes with unbounded continuous state spaces, bounded continuous actions, and polynomially growing rewards: settings that arise naturally in finance, economics, and operations…

Machine Learning · Computer Science 2025-12-18 Hanqing Jin , Renyuan Xu , Yanzhao Yang

Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued It\^{o} calculus machinery. Here it is…

Mathematical Physics · Physics 2023-05-31 Chris D Greenman

We study a stochastic velocity tracking problem for the 2D-Navier-Stokes equations perturbed by a multiplicative Gaussian noise. From a physical point of view, the control acts through a boundary injection/suction device with uncertainty,…

Analysis of PDEs · Mathematics 2023-12-12 Nikolai Chemetov , Fernanda Cipriano

We develop a statistical toolbox for a quantitative model evaluation of stochastic reaction-diffusion systems modeling space-time evolution of biophysical quantities on the intracellular level. Starting from space-time data $X_N(t,x)$, as,…

Methodology · Statistics 2023-07-14 Gregor Pasemann , Carsten Beta , Wilhelm Stannat

We study a nonlinear, pseudomonotone, stochastic diffusion-convection evolution problem on a bounded spatial domain, in any space dimension, with homogeneous boundary conditions and reflection. The additive noise term is given by a…

Analysis of PDEs · Mathematics 2024-12-24 Niklas Sapountzoglou , Yassine Tahraoui , Guy Vallet , Aleksandra Zimmermann

We study the estimation of time-homogeneous drift functions in multivariate stochastic differential equations with known diffusion coefficient, from multiple trajectories observed at high frequency over a fixed time horizon. We formulate…

Machine Learning · Statistics 2026-02-23 Marcos Tapia Costa , Nikolas Kantas , George Deligiannidis

In this paper, we study a multi-objective inverse initial problem with a Nash strategy constraint for forward stochastic reaction-diffusion equations with dynamic boundary conditions, where both the volume and surface equations are…

Analysis of PDEs · Mathematics 2024-10-15 Abdellatif Elgrou , Lahcen Maniar , Omar Oukdach

We consider a distributed stochastic optimization problem in networks with finite number of nodes. Each node adjusts its action to optimize the global utility of the network, which is defined as the sum of local utilities of all nodes.…

Information Theory · Computer Science 2018-07-31 Wenjie Li , Mohamad Assaad

We consider spatially extended conductance based neuronal models with noise described by a stochastic reaction diffusion equation with additive noise coupled to a control variable with multiplicative noise but no diffusion. We only assume a…

Probability · Mathematics 2020-01-16 Martin Sauer , Wilhelm Stannat