ar X iv : m at h / 04 02 43 1 v 3 [ m at h . PR ] 1 8 D ec 2 00 4 Nonclassical stochastic flows and continuous products Boris

ar X iv : 0 80 4 . 43 76 v 1 [ m at h . PR ] 2 8 A pr 2 00 8 fractional brownian flows ∗

We consider stochastic flow on Rn driven by fractional Brownian motion with Hurst parameter H ∈ ( 1 2 , 1), and study tangent flow and the growth of the Hausdorff measure of sub-manifolds of Rn as they evolve under the flow. The main result is a bound on the rate of (global) growth in terms of the (local) Hölder norm of the flow.

ar X iv : m at h / 02 04 28 5 v 1 [ m at h . G T ] 2 3 A pr 2 00 2 FIBER SUMS OF GENUS 2 LEFSCHETZ FIBRATIONS

Using the recent results of Siebert and Tian about the holomorphicity of genus 2 Lefschetz fibrations with irreducible singular fibers, we show that any genus 2 Lefschetz fibration becomes holomorphic after fiber sum with a holomorphic fibration.

ar X iv : 0 80 4 . 43 76 v 2 [ m at h . PR ] 5 A ug 2 00 8 fractional brownian flows ∗

We consider stochastic flow on Rn driven by fractional Brownian motion with Hurst parameter H ∈ ( 1 2 , 1), and study tangent flow and the growth of the Hausdorff measure of sub-manifolds of Rn as they evolve under the flow. The main result is a bound on the rate of (global) growth in terms of the (local) Hölder norm of the flow.

ar X iv : m at h / 04 11 06 2 v 1 [ m at h . O A ] 3 N ov 2 00 4 On automorphisms of type II Arveson systems ( probabilistic approach )

A counterexample to the conjecture that the automorphisms of an arbitrary Arveson system act transitively on its normalized units.

ar X iv : m at h / 05 04 37 3 v 1 [ m at h . Q A ] 1 9 A pr 2 00 5 Lax Operator for the Quantised Orthosymplectic