On the limiting law of the length of the longest common and increasing subsequences in random words

Let $X=(X_i)_{i\ge 1}$ and $Y=(Y_i)_{i\ge 1}$ be two sequences of independent and identically distributed (iid) random variables taking their values, uniformly, in a common totally ordered finite alphabet. Let LCI$_n$ be the length of the longest common and (weakly) increasing subsequence of $X_1\cdots X_n$ and $Y_1\cdots Y_n$. As $n$ grows without bound, and when properly centered and normalized, LCI$_n$ 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

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

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

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