Related papers: On A Class Of Rank-Based Continuous Semimartingale…

We consider stable solutions of semilinear equations in a very general setting. The equation is set on a Polish topological space endowed with a measure and the linear operator is induced by a carr\'e du champs (equivalently, the equation…

Let $\alpha=1/2$, $\theta>-1/2$, and $\nu_0$ be a probability measure on a type space $S$. In this paper, we investigate the stochastic dynamic model for the two-parameter Dirichlet process $\Pi_{\alpha,\theta,\nu_0}$. If $S=\mathbb{N}$, we…

We prove the emergence of stable fluctuations for reaction-diffusion in random environment with Weibull tails. This completes our work around the quenched to annealed transition phenomenon in this context of reaction diffusion. In [9], we…

This paper studies inference in linear models with a high-dimensional parameter matrix that can be well-approximated by a ``spiked low-rank matrix.'' A spiked low-rank matrix has rank that grows slowly compared to its dimensions and nonzero…

We explore a decomposition in which returns on a large class of portfolios relative to the market depend on a smooth non-negative drift and changes in the asset price distribution. This decomposition is obtained using general continuous…

In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent…

Stochastic volatility (SV) models mimic many of the stylized facts attributed to time series of asset returns, while maintaining conceptual simplicity. The commonly made assumption of conditionally normally distributed or…

This paper studies structured node classification on graphs, where the predictions should consider dependencies between the node labels. In particular, we focus on solving the problem for partially labeled graphs where it is essential to…

We give a collection of explicit sufficient conditions for the true martingale property of a wide class of exponentials of semimartingales. We express the conditions in terms of semimartingale characteristics. This turns out to be very…

This paper gives a complete characterization of infinitely divisible semimartingales, i.e., semimartingales whose finite dimensional distributions are infinitely divisible. An explicit and essentially unique decomposition of such…

We study the asymptotic properties of the trajectories of a discrete-time random dynamical system in an infinite-dimensional Hilbert space. Under some natural assumptions on the model, we establish a multiplica-tive ergodic theorem with an…

Statistical properties of the front of a semi-infinite system of single-file diffusion (one dimensional system where particles cannot pass each other, but in-between collisions each one independently follow diffusive motion) are…

In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…

In this paper we study a family of nonlinear (conditional) expectations that can be understood as a diffusion with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued function. We establish…

Taking inspiration from [1, 21, 24], we develop a general framework to deal with the model theory of open incidence structures. In this first paper we focus on the study of systems of points and lines (rank $2$). This has a number of…

The mean-field limit of systems of rank-based interacting diffusions is known to be described by a nonlinear diffusion process. We obtain a similar description at the level of stationary distributions. Our proof is based on explicit…

We describe singular diffusion in bounded subsets $\Omega$ of $\mathbb{R}^n$ by form methods and characterize the associated operator. We also prove positivity and contractivity of the corresponding semigroup. This results in a description…

It is well known that a regular diffusion on an interval $I$ without killing inside is uniquely determined by a canonical scale function $s$ and a canonical speed measure $m$. Note that $s$ is a strictly increasing and continuous function…

We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised…

A general diffusion semimartingale is a one-dimensional path-continuous semimartingale that is also a regular strong Markov process. We say that a continuous semimartingale has the representation property if all local martingales w.r.t. its…