相关论文: An Optimal Skorokhod Embedding for Diffusions

We present some new results on sample path optimality for the ergodic control problem of a class of non-degenerate diffusions controlled through the drift. The hypothesis most often used in the literature to ensure the existence of an a.s.…

Biased Brownian motion of point-size particles in a three-dimensional tube with smoothly varying cross-section is investigated. In the fashion of our recent work [Martens et al., PRE 83,051135] we employ an asymptotic analysis to the…

We consider one-dimensional branching Brownian motion in spatially random branching environment (BBMRE) and show that for almost every realisation of the environment, the distributions of the maximal particle of the BBMRE re-centred around…

In this paper, we consider nonlinear diffusion processes driven by space-time white noises, which have an interpretation in terms of partial differential equations. For a specific choice of coefficients, they correspond to the Landau…

A well-known result across information theory, machine learning, and statistical physics shows that the maximum entropy distribution under a mean constraint has an exponential form called the Gibbs-Boltzmann distribution. This is used for…

The online increasing subsequence problem is a stochastic optimisation task with the objective to maximise the expected length of subsequence chosen from a random series by means of a nonanticipating decision strategy. We study the…

We construct Skorokhod decompositions for diffusions with singular drift and reflecting boundary behavior on open subsets of $\mathbb R^d$ with $C^2$-smooth boundary except for a sufficiently small set. This decomposition holds almost…

Brownian motion is the perpetual irregular motion exhibited by small particles immersed in a fluid. Such random motion of the particles is produced by statistical fluctuations in the collisions they suffer with the molecules of the…

This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…

Discovering relationships between materials' microstructures and mechanical properties is a key goal of materials science. Here, we outline a strategy exploiting Bayesian optimization to efficiently search the multidimensional space of…

We study the ergodic control problem for a class of controlled jump diffusions driven by a compound Poisson process. This extends the results of [SIAM J. Control Optim. 57 (2019), no. 2, 1516-1540] to running costs that are not…

We present discrete-time approximation of optimal control policies for infinite horizon discounted/ergodic control problems for controlled diffusions in $\Rd$\,. In particular, our objective is to show near optimality of optimal policies…

We give a direct derivation of the distribution of the maximum and the location of the maximum of one-sided and two-sided Brownian motion with a negative parabolic drift. The argument uses a relation between integrals of special functions,…

Consider the optimal stopping problem of a one-dimensional diffusion with positive discount. Based on Dynkin's characterization of the value as the minimal excessive majorant of the reward and considering its Riesz representation, we give…

Density matrix embedding theory (DMET) is a quantum embedding theory for strongly correlated systems. From a computational perspective, one bottleneck in DMET is the optimization of the correlation potential to achieve self-consistency,…

We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices,…

We examine the dispersion of Brownian particles in a symmetric two dimensional channel, this classical problem has been widely studied in the literature using the so called Fick-Jacobs' approximation and its various improvements. Most…

We develop an immersed-boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a…

In this paper, we study ergodic backward stochastic differential equations (EBSDEs for short), for which the underlying diffusion is assumed to be multiplicative and of at most linear growth. The fact that the forward process has an…

Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…