441 research outputs found
On the limiting law of the length of the longest common and increasing subsequences in random words
Let and be two sequences of independent
and identically distributed (iid) random variables taking their values,
uniformly, in a common totally ordered finite alphabet. Let LCI be the
length of the longest common and (weakly) increasing subsequence of and . As grows without bound, and when properly
centered and normalized, LCI is shown to converge, in distribution, towards
a Brownian functional that we identify.Comment: Some corrections from the published version are provided, some typos
are also correcte
Asymptotic Cram\'er type decomposition for Wiener and Wigner integrals
We investigate generalizations of the Cram\'er theorem. This theorem asserts
that a Gaussian random variable can be decomposed into the sum of independent
random variables if and only if they are Gaussian. We prove asymptotic
counterparts of such decomposition results for multiple Wiener integrals and
prove that similar results are true for the (asymptotic) decomposition of the
semicircular distribution into free multiple Wigner integrals
Functional macroscopic behavior of weighted random ball model
We consider a generalization of the weighted random ball model. The model is
driven by a random Poisson measure with a product heavy tailed intensity
measure. Such a model typically represents the transmission of a network of
stations with a fading effect. In a previous article, the authors proved the
convergence of the finite-dimensional distributions of related generalized
random fields under various scalings and in the particular case when the fading
function is the indicator function of the unit ball. In this paper, tightness
and functional convergence are investigated. Using suitable moment estimates,
we prove functional convergences for some parametric classes of configurations
under the so-called large ball scaling and intermediate ball scaling.
Convergence in the space of distributions is also discussed
Factorial moments of point processes
We derive joint factorial moment identities for point processes with
Papangelou intensities. Our proof simplifies previous approaches to related
moment identities and includes the setting of Poisson point processes.
Applications are given to random transformations of point processes and to
their distribution invariance properties
Asymptotic Cramér type decomposition for Wiener and Wigner integrals
International audienceWe investigate generalizations of the Cramér theorem. This theorem asserts that a Gaussian random variable can be decomposed into the sum of independent random variables if and only if they are Gaussian. We prove asymptotic counterparts of such decomposition results for multiple Wiener integrals and prove that similar results are true for the (asymptotic) decomposition of the semicircular distribution into free multiple Wigner integrals
Convex comparison inequalities for exponential jump-diffusion processes
International audienceGiven (M_t)_{t∈ℜ_+} and (M*_t)_{t∈ℜ_+} respectively a forward and a backward exponential martingale with jumps and a continuous part, we prove that E [Φ(M_tM*_t)] is non-increasing in t when Φ is a convex function, provided the local characteristics of the stochastic logarithms of (M_t)_{t∈ℜ_+} and of (M*_t)_{t∈ℜ_+} satisfy some comparison inequalities. As an application, we deduce bounds on option prices in markets with jumps, in which the underlying processes need not be Markovian. In this setting the classical propagation of convexity assumption for Markov semigroups (see for instance [El Karaoui, Jeanblanc and Shreve, Math. Finance, vol. 8, 1998]) is not needed
- …