Abstract. We consider free multiple stochastic measures in the combinatorial framework of the lattice of all diagonals of an n-dimensional space. In this free case, one can restrict the analysis to only the noncrossing diagonals. We give definitions of what free multiple stochastic measures are, and calculate them for the free Poisson and free compound Poisson processes. We also derive general ...

The construction of symplectic numerical schemes for stochastic Hamiltonian systems is studied. An approach based on generating functions method is proposed to generate the stochastic symplectic integration of any desired order. In general the proposed symplectic schemes are fully implicit, and they become computationally expensive for mean square orders greater than two. However, for stochasti...

Given a set of nodes, where each pair of nodes is connected by several paths and each path shows a stochastic travel cost with unknown distribution, the multipath Traveling Salesman Problem (TSP) with stochastic travel costs aims at finding an expected minimum Hamiltonian tour connecting all nodes. Under a mild assumption on the unknown probability distribution a deterministic approximation of ...

Algorithms of reinforcement learning usually employ consecutive agent’s actions to construct gradients estimators to adjust agent’s policy. The policy is a result of some kind of stochastic approximation. Because of the slowness of stochastic approximation, such algorithms are usually much too slow to be employed, e.g. in real-time adaptive control. In this paper we analyze the replacing of the...

We propose a new stochastic L-BFGS algorithm and prove a linear convergence rate for strongly convex and smooth functions. Our algorithm draws heavily from a recent stochastic variant of L-BFGS proposed in Byrd et al. (2014) as well as a recent approach to variance reduction for stochastic gradient descent from Johnson and Zhang (2013). We demonstrate experimentally that our algorithm performs ...

Stochastic orders on point processes are partial orders which capture notions like being larger or more variable. Laplace functional ordering of point processes is a useful stochastic order for comparing spatial deployments of wireless networks. It is shown that the ordering of point processes is preserved under independent operations such as marking, thinning, clustering, superposition, and ra...

A fundamental problem in order selection is that one single realization of a stochastic process is used twice, for the estimation of parameters for different model orders and for the selection of the best model order. Parameters are estimated by the minimization of the residual variance; higher model orders with more estimated parameters will always give a smaller residual variance. The purpose...

Levy and Levy (2002, 2004) develop the Prospect and Markowitz stochastic dominance theory with S-shaped and reverse S-shaped utility functions for investors. In this paper, we extend Levy and Levy’s Prospect Stochastic Dominance theory (PSD) and Markowitz Stochastic Dominance theory (MSD) to the first three orders and link the corresponding S-shaped and reverse S-shaped utility functions to the...

The iterative proportional fitting procedure (IPFP) was introduced formally by Deming and Stephan in 1940. For bivariate densities, this procedure has been investigated by Kullback and Rüschendorf. It is well known that the IPFP is a sequence of successive I-projections onto sets of probability measures with fixed marginals. However, when finding the I-projection onto the intersection of arbitr...

Nous étudions comment la récurrence et transience d’ensembles d’espace-temps pour une marche aléatoire branchante sur un graphe dépendent de distribution progéniture. Un ensemble A est appelé récurrent s’il visité infiniment souvent l’événement survie ; il transient si le nombre visites fini presque sûrement. prouvons que μ ν sont deux distributions surcritiques moyennes μ¯<ν¯ alors tout qui l’...