Some parabolic PDEs whose drift is an irregular random noise in space

By Francesco Russo, Gerald Trutnau. 2006

53 citations recorded by the source corpus.

A new class of random partial differential equations of parabolic type is considered, where the stochastic term consists of an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing a realization of the drift (stochastic process), we study existence and uniqueness (in some appropriate sense) of the associated parabolic equation and a probabilistic interpretation is investigated.

Subfields: Control and Systems Engineering, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f950febd71b1e8fec498a02415786f5c82b78059

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. François Delarue
2. R. Diel

In Finance

1. François Delarue
2. R. Diel
3. Daniel Lacker
4. René A. Carmona
5. Franccois Delarue
6. D. Crisan
7. Jean-François Chassagneux
8. Stéphane Menozzi

In Mathematical Physics

1. François Delarue
2. R. Diel
3. Khoa Le
4. Daniel Lacker

Citations in the corpus

• Rough paths and 1d SDE with a time dependent distributional drift: application to polymers (2014, background): “Indeed, much has been said about the long time behavior of the Brownian motion in a time-independent random potential such as the Brownian motion in a Brownian potential, see for example [2, 5, 8, 20, 21, 27, 29].”