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Stochastic hybrid systems involve the coupling between discrete and continuous stochastic processes. They are finding increasing applications in cell biology, ranging from modeling promoter noise in gene networks to analyzing the effects of…

Statistical Mechanics · Physics 2021-05-26 Paul C. Bressloff

In this paper, we are concerned with the classical solvability of a class of second-order Hamilton-Jacobi-Bellman equations (HJB equations) arising from stochastic optimal control problems with linear dynamics and uniformly convex cost…

Optimization and Control · Mathematics 2025-12-19 Jinghua Li , Zhiyong Yu

In this paper we investigate a path dependent optimal control problem on the process space with both drift and volatility controls, with possibly degenerate volatility. The dynamic value function is characterized by a fully nonlinear second…

Optimization and Control · Mathematics 2025-07-23 Jianjun Zhou , Nizar Touzi , Jianfeng Zhang

In this article we study a finite horizon optimal control problem with monotone controls. We consider the associated Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function. We consider the totally discretized problem…

Optimization and Control · Mathematics 2014-07-08 Eduardo A. Philipp , Laura S. Aragone , Lisandro A. Parente

In Stochastic Optimal Control (SOC) one minimizes the average cost-to-go, that consists of the cost-of-control (amount of efforts), cost-of-space (where one wants the system to be) and the target cost (where one wants the system to arrive),…

Statistical Mechanics · Physics 2020-09-29 Vladimir Y. Chernyak , Michael Chertkov , Joris Bierkens , Hilbert J. Kappen

We study an agent's lifecycle portfolio choice problem with stochastic labor income, borrowing constraints and a finite retirement date. Similarly to arXiv:2002.00201, wages evolve in a path-dependent way, but the presence of a finite…

Optimization and Control · Mathematics 2024-02-27 Sara Biagini , Enrico Biffis , Fausto Gozzi , Margherita Zanella

Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…

Methodology · Statistics 2014-05-13 Tianqi Chen , Emily B. Fox , Carlos Guestrin

This article introduces a numerical algorithm that serves as a preliminary step toward solving continuous-time model predictive control (MPC) problems directly without explicit time-discretization. The chief ingredients of the underlying…

Optimization and Control · Mathematics 2024-01-24 Souvik Das , Siddhartha Ganguly , Muthyala Anjali , Debasish Chatterjee

In this paper we study a first extension of the theory of mild solutions for HJB equations in Hilbert spaces to the case when the domain is not the whole space. More precisely, we consider a half-space as domain, and a semilinear…

Optimization and Control · Mathematics 2022-09-30 Alessandro Calvia , Gianluca Cappa , Fausto Gozzi , Enrico Priola

This paper concerns the numerical solution of a fully nonlinear parabolic double obstacle problem arising from a finite portfolio selection with proportional transaction costs. We consider the optimal allocation of wealth among multiple…

Portfolio Management · Quantitative Finance 2017-11-06 Arash Fahim , Wan-Yu Tsai

Path integral quantum Monte Carlo (PIMC) is a method for estimating thermal equilibrium properties of stoquastic quantum spin systems by sampling from a classical Gibbs distribution using Markov chain Monte Carlo. The PIMC method has been…

Quantum Physics · Physics 2021-02-22 Elizabeth Crosson , Aram W. Harrow

Among various rare events, the effective computation of transition paths connecting metastable states in a stochastic model is an important problem. This paper proposes a stochastic optimal control formulation for transition path problems…

Optimization and Control · Mathematics 2023-11-15 Yuan Gao , Jian-Guo Liu , Oliver Tse

We consider the problem of time-optimal path planning for simple nonholonomic vehicles. In previous similar work, the vehicle has been simplified to a point mass and the obstacles have been stationary. Our formulation accounts for a…

Optimization and Control · Mathematics 2021-11-22 Christian Parkinson , Madeline Ceccia

This paper presents multilevel hybrid transport (MLHT) methods for solving the neutral-particle Boltzmann transport equation. The proposed MLHT methods are formulated on a sequence of spatial grids using a multilevel Monte Carlo (MLMC)…

Numerical Analysis · Mathematics 2026-05-12 Vincent N. Novellino , Dmitriy Y. Anistratov

We introduce a stochastic version of the optimal transport problem. We provide an analysis by means of the study of the associated Hamilton-Jacobi-Bellman equation, which is set on the set of probability measures. We introduce a new…

Analysis of PDEs · Mathematics 2024-05-22 Charles Bertucci

A piecewise constant Mayer cost function is used to model optimal control problems in which the state space is partitioned into several regions, each having its own Mayer cost value. In such a context, the standard numerical methods used in…

Optimization and Control · Mathematics 2021-12-02 P. -Y. Bouchet , C. Audet , L. Bourdin

This paper presents a new methodology to craft navigation functions for nonlinear systems with stochastic uncertainty. The method relies on the transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear partial differential…

Robotics · Computer Science 2014-09-23 Matanya B. Horowitz , Joel W. Burdick

An efficient multigrid Monte-Carlo algorithm for calculating the ground state of the hydrogen atom using path integral is presented. The algorithm uses a unigrid approach. The action integral near r=0 is modified so that the correct values…

Quantum Physics · Physics 2007-05-23 Dov Bai

We introduce a new numerical method to approximate the solution of a finite horizon deterministic optimal control problem. We exploit two Hamilton-Jacobi-Bellman PDE, arising by considering the dynamics in forward and backward time. This…

Optimization and Control · Mathematics 2023-04-21 Marianne Akian , Stéphane Gaubert , Shanqing Liu

The Path integral Quantum Control (PiQC) algorithm was recently introduced by Villanueva et al. (2025) as a new approach for computing optimal controls in open and closed quantum systems. Originally proposed for pulse-based quantum control,…

Quantum Physics · Physics 2025-09-30 Peyman Najafi , Aarón Villanueva , Hilbert Kappen