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In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In [21], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in (D p , W p), the space of persistence diagrams equipped with the p-th Wasserstein metric. In… (More)

- M Hairer, J Mattingly
- 2016

We show that the Markov semigroups generated by a large class of singular stochastic PDEs satisfy the strong Feller property. These include for example the KPZ equation and the dynamical Φ 4 3 model. As a corollary, we prove that the Brownian bridge measure is the unique invariant measure for the KPZ equation with periodic boundary conditions.

- A Porporato, P R Kramer, M Cassiani, E Daly, J Mattingly
- Physical review. E, Statistical, nonlinear, and…
- 2011

The time reversal of stochastic diffusion processes is revisited with emphasis on the physical meaning of the time-reversed drift and the noise prescription in the case of multiplicative noise. The local kinematics and mechanics of free diffusion are linked to the hydrodynamic description. These properties also provide an interpretation of the Pope-Ching… (More)

- A Porporato, P R Kramer, M Cassiani, E Daly, J Mattingly
- 2011

The time reversal of stochastic diffusion processes is revisited with emphasis on the physical meaning of the time-reversed drift and the noise prescription in the case of multiplicative noise. The local kinematics and mechanics of free diffusion are linked to the hydrodynamic description. These properties also provide an interpretation of the Pope-Ching… (More)

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