Conformal Skorokhod embeddings and related extremal problems

Extremal Length and Conformal Capacityo

Conformal Capacities and Extremal Metrics

For any non-compact Riemannian manifold M of dimension n ≥ 2 we previously defined a function λM : M×M → R+ = R+∪{+∞] only dependent on the conformal structure of M , and proved that for a class of manifolds containing all the proper subdomains of R, λ 1 n M was a distance on M [F1, F2]. The case of a domain G of R has been the object of several investigations leading to estimations of λG[V1, ....

Skorokhod embeddings, minimality and non-centred target distributions

In this paper we consider the Skorokhod embedding problem for target distributions with non-zero mean. In the zero-mean case, uniform integrability provides a natural restriction on the class of embeddings, but this is no longer suitable when the target distribution is not centred. Instead we restrict our class of stopping times to those which are minimal, and we find conditions on the stopping...

Constructing self-similar martingales via two Skorokhod embeddings

With the help of two Skorokhod embeddings, we construct martingales which enjoy the Brownian scaling property and the (inhomogeneous) Markov property. The second method necessitates randomization, but allows to reach any law with finite moment of order 1, centered, as the distribution of such a martingale at unit time. The first method does not necessitate randomization, but an additional restr...

A unifying class of Skorokhod embeddings: connecting the Azéma–Yor and Vallois embeddings

The Skorokhod embedding problem was first proposed, and then solved, by Skorokhod (1965), and may be described as follows. Given a Brownian motion (Bt) t>0 and a centred target law can we find a ‘small’ stopping time T such that BT has distribution ? Skorokhod gave an explicit construction of the stopping time T in terms of independent random variables, and in doing so showed that any zero-mean...