On stochastic Euler equation in \(\mathbb R^d\). (English) Zbl 0953.60052

Mikulevicius, R.; Valiukevicius, G.

Electron. J. Probab. 5, Paper No. 6, 20 p. (2000).

A stochastic partial differential equation (SPDE) is studied using the associated Euler coordinates obeying to a Euler equation with random forcing in the whole space and represented by a first order SPDE. Including a random perturbation for Euler coordinates a corresponding second order SPDE is derived. There are given and proved eight propositions. The paper is addressed to researchers working in the field of SPDE and interested in equivalent associated stochastic differential equations fulfilled by Euler coordinates.

Reviewer: C.Vârsan (Bucureşti)

MSC:

60H15

Stochastic partial differential equations (aspects of stochastic analysis)

Keywords:

stochastic partial differential equations