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This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle…
We consider optimal control problems for systems governed by mean-field stochastic differential equations, where the control enters both the drift and the diffusion coefficient. We study the relaxed model, in which admissible controls are…
The time evolution of many physical, chemical, and biological systems can be modelled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two…
In this paper, we present a numerical approach to solve the McKean-Vlasov equations, which are distribution-dependent stochastic differential equations, under some non-globally Lipschitz conditions for both the drift and diffusion…
We study interacting particle systems driven by noise, modeling phenomena such as opinion dynamics. We are interested in systems that exhibit phase transitions i.e. non-uniqueness of stationary states for the corresponding McKean-Vlasov…
We study the problem of mean-field control when the state dynamics are given by general systems of forward-backward stochastic differential equations (FBSDEs) with heterogeneous mean-field interactions. Firstly, we introduce a novel…
The viscous drag on a colloidal particle pulled through solution by an optical trap is large enough that on experimentally relavant time scales the mechanical force exerted by the trap is equal and op- posite the viscous drag force. The…
This paper is concerned with optimal control problems for systems governed by mean-field stochastic differential equation, in which the control enters both the drift and the diffusion coefficient. We prove that the relaxed state process,…
Biological sensory systems, from \textit{E.~coli} chemotaxis to sensory neurons in \textit{C.~elegans}, achieve reliable adaptation over wide dynamic ranges despite operating in strongly noisy and overdamped regimes. Here, we present a…
In this paper, we study a linear-quadratic optimal control problem for mean-field stochastic differential equations driven by a Poisson random martingale measure and a multidimensional Brownian motion. Firstly, the existence and uniqueness…
We investigate a quantitative network of gene expression dynamics describing the competence development in Bacillus subtilis. First, we introduce an Onsager-Machlup approach to quantify the most probable transition pathway for both…
The mean field limits of systems of interacting diffusions (also called stochastic interacting particle systems (SIPS)) have been intensively studied since McKean \cite{mckean1966class}. The interacting diffusions pave a way to…
A mean-field method for the hypercubic nearest-neighbor Ising system is introduced and applications to the method are demonstrated. The main idea of this work is to combine the Kadanoff's mean-field approach with the model presented by one…
In this paper, we study multi-species stochastic interacting particle systems and their mean-field McKean-Vlasov partial differential equations (PDEs) in non-convex landscapes. We discuss the well-posedness of the multi-species SDE system,…
This article contributes to a framework for a computational indirect method based on the Pontryagin maximum principle to efficiently solve a class of state constrained time-optimal control problems in the presence of a time-dependent flow…
We analyze a novel class of rough stochastic control problems that allows for a convenient approach to solving pathwise stochastic control problems with both non-anticipative and anticipative controls. We first establish the well-posedness…
We present an approach to the dynamics of interacting particle systems, which allows to derive path integral formulas from purely stochastic considerations. We show that the resulting field theory is a dual version of the standard theory of…
We study particle systems with singular pairwise interactions and non-vanishing diffusion in the mean-field scaling. A classical approach to describing corrections to mean-field behavior is through the analysis of correlation functions. For…
We present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations (SDEs). In particular, we compute the most probable transition path of stochastic equations by…
Motivated by recent interest in graphon mean field games and their applications, this paper provides a comprehensive probabilistic analysis of graphon mean field control (GMFC) problems, where the controlled dynamics are governed by a…