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2018 A new approach for the construction of a Wasserstein diffusion
Victor Marx
Electron. J. Probab. 23: 1-54 (2018). DOI: 10.1214/18-EJP254


We propose in this paper a construction of a diffusion process on the space $\mathcal P_2(\mathbb R)$ of probability measures with a second-order moment. This process was introduced in several papers by Konarovskyi (see e.g. [12]) and consists of the limit as $N$ tends to $+\infty $ of a system of $N$ coalescing and mass-carrying particles. It has properties analogous to those of a standard Euclidean Brownian motion, in a sense that we will precise in this paper. We also compare it to the Wasserstein diffusion on $\mathcal P_2(\mathbb R)$ constructed by von Renesse and Sturm in [22]. We obtain that process by the construction of a system of particles having short-range interactions and by letting the range of interactions tend to zero. This construction can be seen as an approximation of the singular process of Konarovskyi by a sequence of smoother processes.


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Victor Marx. "A new approach for the construction of a Wasserstein diffusion." Electron. J. Probab. 23 1 - 54, 2018.


Received: 17 October 2017; Accepted: 3 December 2018; Published: 2018
First available in Project Euclid: 19 December 2018

zbMATH: 07021680
MathSciNet: MR3896861
Digital Object Identifier: 10.1214/18-EJP254

Primary: 60B12, 60J60, 60K35
Secondary: 60G44, 82B21


Vol.23 • 2018
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