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We analyze the problem of stochastic optimal control of SDEs where the driver includes a self-exciting stochastic process. Due to the non-Markovian nature of the problem, we apply the stochastic maximum principle approach. We derive a…
Analyses of urban scaling laws assume that observations in different cities are independent of the existence of nearby cities. Here we introduce generative models and data-analysis methods that overcome this limitation by modelling…
This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a linear equation in the space…
Controlling large particle systems in collective dynamics by a few agents is a subject of high practical importance, e.g., in evacuation dynamics. In this paper we study an instantaneous control approach to steer an interacting particle…
We study a coupled system of controlled stochastic differential equations (SDEs) driven by a Brownian motion and a compensated Poisson random measure, consisting of a forward SDE in the unknown process $X(t)$ and a \emph{predictive…
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations (PDEs), these emergent patterns sometimes appear as local minimisers of a…
We consider controlled stochastic differential equations (SDEs) with measurable coefficients, a uniformly elliptic diffusion coefficient and an $L_d$-drift. No space-regularity will be assumed for the coefficients. In this framework we…
We propose a new type of SPDEs, singular or with regularized noises, motivated by a study of the fluctuation of the density field in a microscopic interacting particle system. They include a large scaling parameter $N$, which is the ratio…
In this note we provide conditions for local invariance of finite dimensional submanifolds for solutions to stochastic partial differential equations (SPDEs) in the framework of the variational approach. For this purpose, we provide a…
Although the governing equations of many systems, when derived from first principles, may be viewed as known, it is often too expensive to numerically simulate all the interactions they describe. Therefore researchers often seek simpler…
By means of an original approach, called "method of the moving frame", we establish existence, uniqueness and stability results for mild and weak solutions of stochastic partial differential equations (SPDEs) with path dependent…
One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs). We address this problem by taking advantage of recent advances in scientific machine learning and…
In this paper, an epidemic model with spatial dependence is studied and results regarding its stability and numerical approximation are presented. We consider a generalization of the original Kermack and McKendrick model in which the size…
We provide an overview of an optimal control problem within a stochastic model of tumor growth, which includes drug application. The model comprises two stochastic differential equations (SDE) representing the diffusion of nutrient and drug…
Predicting the evolution of diseases is challenging, especially when the data availability is scarce and incomplete. The most popular tools for modelling and predicting infectious disease epidemics are compartmental models. They stratify…
We consider the stochastic control of a semi-linear stochastic partial differential equations (SPDE) of McKean-Vlasov type. Based on a recent novel approach to the Lions derivative for Banach space valued functions, we prove the Gateaux…
In this paper we provide sufficient conditions for stochastic invariance of closed convex cones for stochastic partial differential equations (SPDEs) of jump-diffusion type, and clarify when these conditions are necessary. Our results apply…
Robot navigation around humans can be a challenging problem since human movements are hard to predict. Stochastic model predictive control (MPC) can account for such uncertainties and approximately bound the probability of a collision to…
We consider a stochastic control problem for a class of nonlinear kernels. More precisely, our problem of interest consists in the optimisation, over a set of possibly non-dominated probability measures, of solutions of backward stochastic…
We consider a stochastic optimal control problem for an heat equation with boundary noise and boundary controls. Under suitable assumptions on the coefficients, we prove existence of optimal controls in strong sense by solving the…