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In this paper, we aim to develop the theory of optimal stochastic control for branching diffusion processes where both the movement and the reproduction of the particles depend on the control. More precisely, we study the problem of…

Probability · Mathematics 2016-09-19 Julien Claisse

In this paper, we prove a maximum principle for the general multi-term space-time-fractional transport equation and apply it for establishing uniqueness of solution to an initial-boundary-value problem for this equation. We also derive some…

Analysis of PDEs · Mathematics 2021-03-12 Yuri Luchko , Anna Suzuki , Masahiro Yamamoto

Preservation of the maximum principle is studied for the combination of the linear finite element method in space and the $\theta$-method in time for solving time dependent anisotropic diffusion problems. It is shown that the numerical…

Numerical Analysis · Mathematics 2013-10-23 Xianping Li , Weizhang Huang

A coordinate-free proof of the Maximum Principle is provided in the specific case of an optimal control problem with fixed time. Our treatment heavily relies on a special notion of variation of curves that consist of a concatenation of…

Differential Geometry · Mathematics 2007-05-23 B. Langerock

Existing approaches to diffusion-based inverse problem solvers frame the signal recovery task as a probabilistic sampling episode, where the solution is drawn from the desired posterior distribution. This framework suffers from several…

Machine Learning · Computer Science 2024-12-24 Henry Li , Marcus Pereira

The global existence of bounded solutions to reaction-diffusion systems with fractional diffusion in the whole space $\mathbb R^N$ is investigated. The systems are assumed to preserve the non-negativity of initial data and to dissipate…

Analysis of PDEs · Mathematics 2025-02-25 Phuoc-Tai Nguyen , Bao Quoc Tang

This paper introduces a new recursive stochastic optimal control problem driven by a forward-backward stochastic differential equations (FBSDEs), where the ter?minal time varies according to the constraints of the state of the forward…

Optimization and Control · Mathematics 2023-04-17 Jiaqi Wang , Shuzhen Yang

In this article we derive a strong version of the Pontryagin Maximum Principle for general nonlinear optimal control problems on time scales in finite dimension. The final time can be fixed or not, and in the case of general boundary…

Optimization and Control · Mathematics 2013-02-15 Loïc Bourdin , Emmanuel Trélat

Consider a set of discounted optimal stopping problems for a one-parameter family of objective functions and a fixed diffusion process, started at a fixed point. A standard problem in stochastic control/optimal stopping is to solve for the…

Probability · Mathematics 2010-05-04 David Hobson , Martin Klimmek

The article is devoted to the problem of applying the maximum principle for finding optimal control parameters in simulation tasks of interest for a variety of engineering and industrial systems and processes. Especially important is the…

Optimization and Control · Mathematics 2018-03-28 Ivan V. Kazachkov

In this paper, we are interested in a general equation that has finite speed of propagation compatible with Einstein's theory of special relativity. This equation without external force fields has been derived recently by means of optimal…

Analysis of PDEs · Mathematics 2015-08-18 Manh Hong Duong

We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod…

Probability · Mathematics 2017-11-27 Tiziano De Angelis , Erik Ekström

We establish necessary conditions of optimality for discrete-time infinite-horizon optimal control in presence of constraints at infinity. These necessary conditions are in form of weak and strong Pontryagin principles. We use a functional…

Dynamical Systems · Mathematics 2015-11-09 Joel Blot , Thoi Ngo

This work examines a class of switching jump diffusion processes. The main effort is devoted to proving the maximum principle and obtaining the Harnack inequalities. Compared with the diffusions and switching diffusions, the associated…

Probability · Mathematics 2018-10-02 Xiaoshan Chen , Zhen-Qing Chen , Ky Tran , George Yin

We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…

Computational Finance · Quantitative Finance 2012-10-10 Timothy C. Johnson

We consider an impulse control problem in infinite horizon. To solve this problem, we extend to the infinite horizon case results of double barrier reflected backward stochastic differential equations. The properties of the Snell envelope…

Optimization and Control · Mathematics 2012-02-03 Rim Amami

We consider a terminal control problem for processes governed by a nonlinear system of fractional ODEs. In order to show existence of the control, we first consider the linear counterpart of the system and reprove a number of classical…

Optimization and Control · Mathematics 2022-12-27 Maja Jolić , Sanja Konjik , Darko Mitrović

In this work we prove a strong maximum principle for fractional elliptic problems with mixed Dirichlet-Neumann boundary data which extends the one proved by J. D\'avila to the fractional setting. In particular, we present a comparison…

Analysis of PDEs · Mathematics 2021-11-10 Rafael López-Soriano , Alejandro Ortega

In this paper, we solve an open problem and obtain a general maximum principle for a stochastic optimal control problem where the control domain is an arbitrary non-empty set and all the coefficients (especially the diffusion term and the…

Optimization and Control · Mathematics 2023-02-08 Weijun Meng , Jingtao Shi , Tianxiao Wang , Ji-Feng Zhang

The aim of the paper is to study an optimal control problem on infinite horizon for an infinite dimensional integro-differential equation with completely monotone kernelskernels, where we assume that the noise enters the system when we…

Optimization and Control · Mathematics 2016-10-31 Elisa Mastrogiacomo