#### Title

Weak solutions to stochastic differential equations with discontinuous drift in Hilbert space. Stochastic processes, physics and geometry: new interplays, II

#### Document Type

Conference Proceeding

#### Publication Date

1-1-2000

#### Publication Title

Canadian Mathematical Society Conference Proceedings

#### Conference Name

Canadian Mathematical Society Conference

#### Abstract

Professor Sergio Albeverio has been interested in solutions of infinite dimensional stochastic differential equations with values in C([0, T], R^{zd}) motivated by applications to physics ([1], [2]). Leha and Ritter in [6] have studied the existence problem in C([0, T], H^{w}). Our purpose here is to extend the latter work by weakening the assumptions on the potential, using techniques developed in our earlier work. More precisely, we study the problem of the existence of weak solutions for SDE's with discontinuous drift in a Hilbert space H. The discontinuity is modeled by a countable family of real valued functions. The solution has finite dimensional Galerkin approximation and is realized in the space of continuous functions with values in H, where H is endowed with its weak topology. Th.is work extends a result in [6] and also shows that under the assumptions in [6] both, the Galerkin approximation and the infinite dimensional approximation of [6] produce solutions with identical laws.

#### Rights Statement

© 2000 American Mathematical Society

#### Recommended Citation

Gawarecki, Leszek and Mandrekar, Vidyadhar, "Weak solutions to stochastic differential equations with discontinuous drift in Hilbert space. Stochastic processes, physics and geometry: new interplays, II" (2000). *Mathematics Presentations And Conference Materials*. 2.

https://digitalcommons.kettering.edu/mathematics_conference/2

## Comments

ISBN 9780821819609 Volume: 29. Leipzig Germany, 1999