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Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…

Systems and Control · Electrical Eng. & Systems 2025-08-12 Alexandros E. Tzikas , Lukas Fiechtner , Arec Jamgochian , Mykel J. Kochenderfer

Dynamic phenomena in social and biological sciences can often be modeled by employing reaction-diffusion equations. When addressing the control of these modes, from a mathematical viewpoint one of the main challenges is that, because of the…

Optimization and Control · Mathematics 2020-06-02 Domènec Ruiz-Balet , Enrique Zuazua

Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an…

Statistical Mechanics · Physics 2024-09-18 Julia Sanders , Marco Baldovin , Paolo Muratore-Ginanneschi

We are concerned with scaling limits of the solutions to stochastic differential equations with stationary coefficients driven by Poisson random measures and Brownian motions. We state an annealed convergence theorem, in which the limit…

Probability · Mathematics 2008-12-26 Remi Rhodes , Vincent Vargas

We study the long-range asymptotic behavior for an out-of-equilibrium countable one-dimensional system of Brownian particles interacting through their rank-dependent drifts. Focusing on the semi-infinite case, where only the leftmost…

Probability · Mathematics 2017-08-10 Manuel Cabezas , Amir Dembo , Andrey Sarantsev , Vladas Sidoravicius

Aiming for more realistic optimal dividend policies, we consider a stochastic control problem with linearly bounded control rates using a performance function given by the expected present value of dividend payments made up to ruin. In a…

Probability · Mathematics 2020-07-14 Jean-François Renaud , Clarence Simard

We obtain exact asymptotic results for the disorder averaged persistence of a Brownian particle moving in a biased Sinai landscape. We employ a new method that maps the problem of computing the persistence to the problem of finding the…

Statistical Mechanics · Physics 2009-11-07 Satya N. Majumdar , Alain Comtet

This paper considers the joint compression of a pair of correlated sources, where the encoder is allowed to access only one of the sources. The objective is to recover both sources under separate distortion constraints for each source while…

Information Theory · Computer Science 2024-11-07 Huiyuan Yang , Yuxuan Shi , Shuo Shao , Xiaojun Yuan

This paper concerns the use of asymptotic expansions for the efficient solving of forward and inverse problems involving a nonlinear singularly perturbed time-dependent reaction--diffusion--advection equation. By using an asymptotic…

Numerical Analysis · Mathematics 2023-02-15 Dmitrii Chaikovskii , Ye Zhang

We prove convergence of the proximal policy gradient method for a class of constrained stochastic control problems with control in both the drift and diffusion of the state process. The problem requires either the running or terminal cost…

Optimization and Control · Mathematics 2025-05-27 Ashley Davey , Harry Zheng

We study the second-order asymptotics around the superdiffusive strong law~\cite{MMW} of a multidimensional driftless diffusion with oblique reflection from the boundary in a generalised parabolic domain. In the unbounded direction we prove…

Probability · Mathematics 2024-12-20 Aleksandar Mijatović , Isao Sauzedde , Andrew Wade

Consider compound Poisson processes with negative drift and no negative jumps, which converge to some spectrally positive L\'evy process with non-zero L\'evy measure. In this paper we study the asymptotic behavior of the local time process,…

Probability · Mathematics 2013-05-24 Amaury Lambert , Florian Simatos

We introduce a Langevin equation characterized by a time dependent drift. By assuming a temporal power-law dependence of the drift we show that a great variety of behavior is observed in the dynamics of the variance of the process. In…

Statistical Mechanics · Physics 2009-10-31 Fabrizio Lillo , Rosario N. Mantegna

This paper deals with the analysis of the internal control with constraint of positive kind of a parabolic PDE with nonlinear diffusion when the time horizon is large enough. The minimal controllability time will be strictly positive. We…

Analysis of PDEs · Mathematics 2021-04-12 Miguel R. Nuñez-Chávez

We consider the classical Merton problem of lifetime consumption-portfolio optimization problem with small proportional transaction costs. The first order term in the asymptotic expansion is explicitly calculated through a singular ergodic…

Optimization and Control · Mathematics 2013-06-18 H. Mete Soner , Nizar Touzi

This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…

Numerical Analysis · Mathematics 2025-01-14 Gouranga Mallik , Ramesh Chandra Sau

We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…

Optimization and Control · Mathematics 2024-04-04 Christoph Buchheim , Alexandra Grütering , Christian Meyer

We consider the asymptotic distribution of a cell in a 2 x ... x 2 contingency table as the fixed marginal totals tend to infinity. The asymptotic order of the cell variance is derived and a useful diagnostic is given for determining…

Statistics Theory · Mathematics 2018-04-17 Quan Zhou

The Sierpinski gasket is known to support an exotic stochastic process called the asymptotically one-dimensional diffusion. This process displays local anisotropy, as there is a preferred direction of motion which dominates at the…

Probability · Mathematics 2019-03-13 Ben Hambly , Weiye Yang

We show a probabilistic functional limit result for one-dimensional diffusion processes that are reflected at an elastic boundary which is a function of the reflection local time. Such processes are constructed as limits of a sequence of…

Probability · Mathematics 2019-06-27 Dirk Becherer , Todor Bilarev , Peter Frentrup