Convergence of U-statistics indexed by a random walk to stochastic integrals of a Levy sheet

We establish limit theorems for U-statistics indexed by a random walk on Z^d and we express the limit in terms of some Levy sheet Z(s,t). Under some hypotheses, we prove that the limit process is Z(t,t) if the random walk is transient or null-recurrent ant that it is some stochastic integral with respect to Z when the walk is positive recurrent. We compare our results with results for random walks in random scenery.Comment: 38 page

Heterogeneity of Investors and Asset Pricing in a Risk-Value World

Decision Making Under Risk, Asset Pricing, Convexity of Pricing Kernel, Heterogeneity of Investors

Stable limit theorem for U-statistic processes indexed by a random walk

Let (Sn)n2N be a random walk in the domain of attraction of an a -stable Lévy process and ( (n))n2N a sequence of iid random variables (called scenery). We want to investigate U-statistics indexed by the random walk Sn, that is Un := P 1 i<j n h( (Si); (Sj )) for some symmetric bivariate function h. We will prove the weak convergence without the assumption of finite variance. Additionally, under the assumption of finite moments of order greater than two, we will establish a law of the iterated logarithm for the U-statistic Un

Dopamine-functionalized polymers

The invention is directed to a tissue-adhesive polymer comprising at least one polymeric chain functionalized with an ArOH group, wherein said ArOH represents a hydroxyl-substituted aromatic group which is bound to said polymeric chain with an amide, urethane, thiourethane or urea bond, optionally Via a spacer. The ArOH can be positioned at one or more termini of said polymeric chain, at the backbone of the polymeric chain according to formula lb, or both. The ArOH can be based on a compound such as dopamine, DL-DOPA, L-DOPA, D-DOPA, tyramine, noradrenaline and/or serotonin. In addition, the invention is directed to a caprolactam blocked hydroxyl-substituted aromatic compound, suitable for the preparation of the tissue-adhesive polymer and to the method for the preparation of the tissue-adhesive polymer