Related papers: A Correction to "Dynkin Games Via Dirichlet Forms …
In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of…
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…
Controllable diffusion generation often relies on various heuristics that are seemingly disconnected without a unified understanding. We bridge this gap with Diffusion Controller (DiffCon), a unified control-theoretic view that casts…
We consider an optimal control problem where the average welfare of weakly interacting agents is of interest. We examine the mean-field control problem as the fluid approximation of the N-agent control problem with the setup of finite-state…
This paper studies regularity property of the value function for an infinite-horizon discounted cost impulse control problem, where the underlying controlled process is a multidimensional jump diffusion with possibly `infinite-activity'…
In this paper we prove a version of the maximum principle, in the sense of Pontryagin, for the optimal control of a finite dimensional stochastic differential equation, driven by a multidimensional Wiener process. We drop the usual…
The paper studies Dirichlet forms on the classical Wiener space and the Wiener space over non-compact complete Riemannian manifolds. The diffusion operator is almost everywhere an unbounded operator on the Cameron--Martin space. In…
Diffusion models exhibited tremendous progress in image and video generation, exceeding GANs in quality and diversity. However, they are usually trained on very large datasets and are not naturally adapted to manipulate a given input image…
We study a time-inconsistent singular stochastic control problem for a general one-dimensional diffusion, where time-inconsistency arises from a non-exponential discount function. To address this, we adopt a game-theoretic framework and…
We show that a one-dimensional regular continuous Markov process \(\X\) with scale function \(s\) is a Feller--Dynkin process precisely if the space transformed process \(s (X)\) is a martingale when stopped at the boundaries of its state…
We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the…
We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals --…
We consider a general one-dimensional overdamped diffusion model described by the It\^{o} stochastic differential equation (SDE) ${dX_t=\mu(X_t,t)dt+\sigma(X_t,t)dW_t}$, where $W_t$ is the standard Wiener process. We obtain a specific…
In this article, we study the global-in-time well-posedness of second order mean field games (MFGs) with both nonlinear drift functions simultaneously depending on the state, distribution and control variables, and the diffusion term…
We propose diffusion-like equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which,…
Mean Field Games (MFG) theory describes strategic interactions in differential games with a large number of small and indistinguishable players. Traditionally, the players' control impacts only the drift term in the system's dynamics,…
We study the optimal control of mean-field systems with heterogeneous and asymmetric interactions. This leads to considering a family of controlled Brownian diffusion processes with dynamics depending on the whole collection of marginal…
In a probabilistic mean-field game driven by a linear diffusion an individual player aims to minimize an ergodic long-run cost by controlling the diffusion through a pair of -- increasing and decreasing -- c\`adl\`ag processes, while he is…
In this paper, we consider the approximate controllability of partial differential equations with time derivatives of non-integer order via boundary control. We first show the unique existence of the solution under smooth boundary…
In this paper, we consider the optimal control problem in a 3D flow model for incompressible rigid-viscoplastic media of the Bingham kind with homogeneous Dirichlet boundary conditions and a given cost functional. On the basis of methods of…