We investigate the optimal alignment of two independent random sequences of length n. We provide a polynomial lower bound for the probability of the optimal alignment to be macroscopically non-unique. We furthermore establish a connection between the transversal fluctuation and macroscopic non-uniqueness.
Let be a symmetric semigroup of stable measures on a homogeneous group, with smooth Lévy measure. Applying Malliavin calculus for jump processes we prove that the measures have smooth densities.
Mathematical models for financial asset prices which include, for example, stochastic volatility or jumps are incomplete in that derivative securities are generally not replicable by trading in the underlying. In earlier work [Proc. R. Soc. London, 2004], the first author provided a geometric condition under which trading in the underlying and a finite number of vanilla options completes the market. We complement this result in several ways. First, we show that the geometric condition is not necessary...
The brownian web (BW), which developed from the work of Arratia and then Tóth and Werner, is a random collection of paths (with specified starting points) in one plus one dimensional space–time that arises as the scaling limit of the discrete web (DW) of coalescing simple random walks. Two recently introduced extensions of the BW, the brownian net (BN) constructed by Sun and Swart, and the dynamical brownian web (DyBW) proposed by Howitt and Warren, are (or should be) scaling limits of corresponding...
Given a substochastic kernel from a measurable space into itself one considers for a pair of finite measures on the following sequences:
The L-decomposable and the bi-decomposable models are two families of distributions on the set of all permutations of the first positive integers. Both of these models are characterized by collections of conditional independence relations. We first compute a Markov basis for the L-decomposable model, then give partial results about the Markov basis of the bi-decomposable model. Using these Markov bases, we show that not all bi-decomposable distributions can be approximated arbitrarily well by...
Quantum trajectories are solutions of stochastic differential equations obtained when describing the random phenomena associated to quantum continuous measurement of open quantum system. These equations, also called Belavkin equations or Stochastic Master equations, are usually of two different types: diffusive and of Poisson-type. In this article, we consider more advanced models in which jump–diffusion equations appear. These equations are obtained as a continuous time limit of martingale problems...