Marcinkiewicz-type strong law of large numbers for double arrays of pairwise independent random variables.
Marginal problem, statistical estimation, and Möbius formula
A solution to the marginal problem is obtained in a form of parametric exponential (Gibbs–Markov) distribution, where the unknown parameters are obtained by an optimization procedure that agrees with the maximum likelihood (ML) estimate. With respect to a difficult performance of the method we propose also an alternative approach, providing the original basis of marginals can be appropriately extended. Then the (numerically feasible) solution can be obtained either by the maximum pseudo-likelihood...
Marginalization in models generated by compositional expressions
In the framework of models generated by compositional expressions, we solve two topical marginalization problems (namely, the single-marginal problem and the marginal-representation problem) that were solved only for the special class of the so-called “canonical expressions”. We also show that the two problems can be solved “from scratch” with preliminary symbolic computation.
Marginalization in multidimensional compositional models
Efficient computational algorithms are what made graphical Markov models so popular and successful. Similar algorithms can also be developed for computation with compositional models, which form an alternative to graphical Markov models. In this paper we present a theoretical basis as well as a scheme of an algorithm enabling computation of marginals for multidimensional distributions represented in the form of compositional models.
Marked continuous-time Markov chain modelling of burst behaviour for single ion channels.
Marked excursions and random trees
Market completion using options
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...
Marking (1, 2) points of the brownian web and applications
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...
Markoff-Ketten bei sich füllenden Löchern im Zustandsraum
Given a substochastic kernel from a measurable space into itself one considers for a pair of finite measures on the following sequences:
Markov bases of conditional independence models for permutations
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...
Markov chain approximations to symmetric diffusions
Markov chain comparison.
Markov chain intersections and the loop-erased walk
Markov chain model of phytoplankton dynamics
A discrete-time stochastic spatial model of plankton dynamics is given. We focus on aggregative behaviour of plankton cells. Our aim is to show the convergence of a microscopic, stochastic model to a macroscopic one, given by an evolution equation. Some numerical simulations are also presented.
Markov chain small-world model with asymmetric transition probabilities.
Markov chains approximation of jump–diffusion stochastic master equations
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...
Markov chains as Evans-Hudson diffusions in Fock space
Markov Chains, Riesz Transforms and Lipschitz Maps.
Markov chains with quasi-Toeplitz transition matrix: Applications.
Markov chains with transition delta-matrix: Ergodicity conditions, invariant probability measures and applications.