2 papers
math.DG2005
Hilbert-Schmidt groups as infinite-dimensional Lie groups and their Riemannian geometry
Maria Gordina
We describe the exponential map from an infinite-dimensional Lie algebra to an infinite-dimensional group of operators on a Hilbert space. Notions of differential geometry are intr…
math.PR2005
Infinite dimensional stochastic differential equations of Ornstein-Uhlenbeck type
Siva R. Athreya, Richard F. Bass, Maria Gordina +1
We consider the operator $$\sL f(x)=\tfrac12 \sum_{i,j=1}^\infty a_{ij}(x)\frac{\del^2 f}{\del x_i \del x_j}(x)-\sum_{i=1}^\infty \lam_i x_i b_i(x) \frac{\del f}{\del x_i}(x).$$ We…