Electronic Journal of Probability
- Electron. J. Probab.
- Volume 23 (2018), paper no. 124, 54 pp.
A new approach for the construction of a Wasserstein diffusion
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. ) 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 . 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.
Electron. J. Probab., Volume 23 (2018), paper no. 124, 54 pp.
Received: 17 October 2017
Accepted: 3 December 2018
First available in Project Euclid: 19 December 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J60: Diffusion processes [See also 58J65] 60B12: Limit theorems for vector-valued random variables (infinite- dimensional case)
Secondary: 60G44: Martingales with continuous parameter 82B21: Continuum models (systems of particles, etc.)
Marx, Victor. A new approach for the construction of a Wasserstein diffusion. Electron. J. Probab. 23 (2018), paper no. 124, 54 pp. doi:10.1214/18-EJP254. https://projecteuclid.org/euclid.ejp/1545188691