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The proportional likelihood ratio order and applications.

Héctor M. Ramos Romero, Miguel Angel Sordo Díaz (2001)

Qüestiió

In this paper, we introduce a new stochastic order between continuous non-negative random variables called the PLR (proportional likelihood ratio) order, which is closely related to the usual likelihood ratio order. The PLR order can be used to characterize random variables whose logarithms have log-concave (log-convex) densities. Many income random variables satisfy this property and they are said to have the IPLR (increasing proportional likelihood ratio) property (DPLR property). As an application,...

The quenched invariance principle for random walks in random environments admitting a bounded cycle representation

Jean-Dominique Deuschel, Holger Kösters (2008)

Annales de l'I.H.P. Probabilités et statistiques

We derive a quenched invariance principle for random walks in random environments whose transition probabilities are defined in terms of weighted cycles of bounded length. To this end, we adapt the proof for random walks among random conductances by Sidoravicius and Sznitman (Probab. Theory Related Fields129 (2004) 219–244) to the non-reversible setting.

The rate of convergence for iterated function systems

Maciej Ślęczka (2011)

Studia Mathematica

Iterated function systems with place-dependent probabilities are considered. It is shown that the rate of convergence of transition probabilities to a unique invariant measure is geometric.

The rate of convergence for spectra of GUE and LUE matrix ensembles

Friedrich Götze, Alexander Tikhomirov (2005)

Open Mathematics

We obtain optimal bounds of order O(n −1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution functions of random matrices from the GUE and LUE, respectively.

The rate of convergence of option prices when general martingale discrete-time scheme approximates the Black-Scholes model

Yuliya Mishura (2015)

Banach Center Publications

We take the martingale central limit theorem that was established, together with the rate of convergence, by Liptser and Shiryaev, and adapt it to the multiplicative scheme of financial markets with discrete time that converge to the standard Black-Scholes model. The rate of convergence of put and call option prices is shown to be bounded by n - 1 / 8 . To improve the rate of convergence, we suppose that the increments are independent and identically distributed (but without binomial or similar restrictions...

The rate of escape for random walks on polycyclic and metabelian groups

Russ Thompson (2013)

Annales de l'I.H.P. Probabilités et statistiques

We use subgroup distortion to determine the rate of escape of a simple random walk on a class of polycyclic groups, and we show that the rate of escape is invariant under changes of generating set for these groups. For metabelian groups, we define a stronger form of subgroup distortion which applies to non-finitely generated subgroups. Under this hypothesis, we compute the rate of escape for certain random walks on some abelian-by-cyclic groups via a comparison to the toppling of a dissipative abelian...

The Ray space of a right process

Ronald K. Getoor, Michael J. Sharpe (1975)

Annales de l'institut Fourier

Let X be a process with state space E satisfying (a somewhat relaxed version of) Meyer’s “hypothèses droites”. Then by introducing a new topology (called the Ray topology) on E and a compactification F of E in the Ray topology one can regard X as a Ray process. However, this construction depends on the choice of an arbitrary uniformity on E and not just the topology of E . We show that the Ray topology is independent of the choice of this uniformity. We then introduce a space R (the Ray space) which...

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