ar X iv : 0 90 7 . 41 78 v 1 [ m at h . PR ] 2 3 Ju l 2 00 9 An Introduction to Stochastic PDEs

ar X iv : 0 70 6 . 23 90 v 1 [ m at h . PR ] 1 6 Ju n 20 07 STOCHASTIC PARABOLIC EQUATIONS OF FULL SECOND ORDER

A procedure is described for defining a generalized solution for stochastic differential equations using the Cameron-Martin version of the Wiener Chaos expansion. Existence and uniqueness of this Wiener Chaos solution is established for parabolic stochastic PDEs such that both the drift and the diffusion operators are of the second order.

ar X iv : 0 90 7 . 29 64 v 1 [ m at h . FA ] 1 7 Ju l 2 00 9 THE NORM OF A TRUNCATED TOEPLITZ OPERATOR

We prove several lower bounds for the norm of a truncated Toeplitz operator and obtain a curious relationship between the H and H∞ norms of functions in model spaces.

ar X iv : 0 90 4 . 31 78 v 1 [ m at h . FA ] 2 1 A pr 2 00 9 TREE METRICS AND THEIR LIPSCHITZ - FREE SPACES

We compute the Lipschitz-free spaces of subsets of the real line and characterize subsets of metric trees by the fact that their Lipschitz-free space is isometric to a subspace of L1.

ar X iv : 0 90 7 . 20 23 v 1 [ m at h - ph ] 1 2 Ju l 2 00 9 Menelaus relation and Fay ’ s trisecant formula are associativity equations

It is shown that the celebrated Menelaus relation and Fay's trisecant formula similar to the WDVV equation are associativity conditions for structure constants of certain three-dimensional algebra.

ar X iv : 0 70 7 . 33 03 v 1 [ m at h . O A ] 2 3 Ju l 2 00 7 OPERATOR - VALUED FRAMES