Related papers: Stochastic homogenization for Hamilton-Jacobi-Bell…
The quasi-periodic homogenization for some classes of first-order Hamilton-Jaconi-Bellman equation is studied in this paper. The cell problem of the quasi-periodic homogenization satisfies the non-resonance condition, under which the…
In this paper, we propose and study the stochastic path-dependent Hamilton-Jacobi-Bellman (SPHJB) equation that arises naturally from the optimal stochastic control problem of stochastic differential equations with path-dependence and…
We prove comparison principle for viscosity solutions of a Hamilton-Jacobi-Bellman equation in a strong coupling regime considering a stationary and a time-dependent version of the equation. We consider a Hamiltonian that has a…
This paper investigates a class of multiscale stochastic control problems driven by $\alpha$-stable L\'evy noises, where the controlled dynamics evolve across separate slow and fast time scales. The associated value functions are governed…
Unbounded stochastic control problems may lead to Hamilton-Jacobi-Bellman equations whose Hamiltonians are not always defined, especially when the diffusion term is unbounded with respect to the control. We obtain existence and uniqueness…
In this paper we derive a constrained Hamilton-Jacobi equation with obstacle from a discrete non-linear integro-differential model of population dynamics, with exponentially decaying mutation kernel. The exponential decay of the kernel…
We study the regularity properties of integro-partial differential equations of Hamilton-Jocobi-Bellman type with terminal condition, which can be interpreted through a stochastic control system, composed of a forward and a backward…
We study a cell problem arising in homogenization for a Hamilton-Jacobi equation whose Hamiltonian is not coercive. We introduce a generalized notion of effective Hamiltonians by approximating the equation and characterize the solvability…
Stochastic optimal control problems for Hamiltonian dynamics on graphs have wide-ranging applications in mechanics and quantum field theory, particularly in systems with graph-based structures. In this paper, we establish the existence and…
We study a stochastic optimal control problem with the state constrained to a smooth, compact domain. The control influences both the drift and a possibly degenerate, control-dependent dispersion matrix, leading to a fully nonlinear,…
Continuous-time reinforcement learning offers an appealing formalism for describing control problems in which the passage of time is not naturally divided into discrete increments. Here we consider the problem of predicting the distribution…
The ergodic control problem for a non-degenerate controlled diffusion controlled through its drift is considered under a uniform stability condition that ensures the well-posedness of the associated Hamilton-Jacobi-Bellman (HJB) equation. A…
Recent studies have extended the use of the stochastic Hamilton-Jacobi-Bellman (HJB) equation to include complex variables for deriving quantum mechanical equations. However, these studies often assume that it is valid to apply the HJB…
We study the exploratory Hamilton--Jacobi--Bellman (HJB) equation arising from the entropy-regularized exploratory control problem, which was formulated by Wang, Zariphopoulou and Zhou (J. Mach. Learn. Res., 21, 2020) in the context of…
This paper deals with the periodic homogenization of nonlocal parabolic Hamilton-Jacobi equations with superlinear growth in the gradient terms. We show that the problem presents different features depending on the order of the nonlocal…
We consider first-passage percolation with positive, stationary-ergodic weights on the square lattice $\mathbb{Z}^d$. Let $T(x)$ be the first-passage time from the origin to a point $x$ in $\mathbb{Z}^d$. The convergence of the scaled…
We prove, under some assumptions, the existence of correctors for the stochastic homoge-nization of of " viscous " possibly degenerate Hamilton-Jacobi equations in stationary ergodic media. The general claim is that, assuming knowledge of…
We extend the Barles-Perthame procedure of semi-relaxed limits of viscosity solutions of Hamilton-Jacobi equations of the type f - lambda H f = h. The convergence result allows for equations on a `converging sequence of spaces' as well as…
We study the rate of convergence of $u^\epsilon$, as $\epsilon \to 0+$, to $u$ in periodic homogenization of Hamilton-Jacobi equations. Here, $u^\epsilon$ and $u$ are viscosity solutions to the oscillatory Hamilton-Jacobi equation and its…
We consider the specified stochastic homogenization of first order evolutive Hamilton-Jacobi equations on a very simple junction, i.e the real line with a junction at the origin. Far from the origin, we assume that the considered…