Volume 16, Issue 1

We consider an alloy type potential on an infinite metric graph. We assume a covering condition on the single site potentials. For random Schrödingers operator associated with the alloy type potential restricted to finite volume subgraphs we prove a Wegner estimate which reproduces the modulus of continuity of the single site distribution measure. The Wegner constant is independent of the energy.

In this paper, we will continue to study a mathematical tool which can be used on a financial market by a “small” investor who possesses some information on the price process. We extend here the results given for hedging strategies under a fixed terminal time to the case of a random terminal time. We extensively use the backward stochastic differential equation theory to give sufficient condition to compare the strategies of an insider trader and the non insider one for an American contingent claim.

Consider a linear stochastic differential equation With time delay driven by a fractional Brownian motion . We investigate the asymptotic properties of the maximum likelihood estimator of the parameter θ = ( a, b ).

We consider some classes of pre-Gaussian random processes. We obtain several theorems on estimation of distribution of the supremum of these processes both on pseudometric space ( T , ρ ) and on ℝ.

Let ( B s ) s≥t be Brownian motion, t be the starting moment, B t = x , EB s = x , DB s = s – t . Let T ≥ t be a fixed time-horizon, and lower( s ), upper( s ) be two smooth real functions, defined for s ∈ [ t ; T ], such that lower( s ) < upper( s ) for all s ∈ [ t ; T ), lower( t ) ≤ x ≤ upper ( t ). Finally, let τ = inf { s ∈ [ t ; T )| B s = lower( s ) or B s = upper( s )}, where inf ø = T , and let = {B τ = upper( τ )}, = { B τ = lower( τ )}, . We obtain explicit formulae for P t, x (), P t, x (), and P t, x () in two special cases: square-root boundaries with a natural horizon and arcsine boundaries with no horizon.