On the lower bound of the spectral norm of symmetric random matrices with independent entries.
On the lower classes of some mixed fractional Gaussian processes with two logarithmic factors.
On the marginal laws of one-dimensional stochastic integrals with uniformly elliptic integrand
On the Markov chain central limit theorem.
On the martingale problem for super-brownian motion
On the martingales obtained by an extension due to Saisho, Tanemura and Yor of Pitman's theorem
On the Mathematical Theory of Records
In the present work, we briefly analyze the development of the mathematical theory of records. We first consider applications associated with records. We then view distributional and limit results for record values and times. We further present methods of generation of continuous records. In the end of this work, we discuss some tests based on records.
On the Maximal Lévy-Ottaviani Inequality for Sums of Independent and Dependent Random Vectors
We prove that the sums of independent random vectors satisfy , t ≥ 0.
On the Maximum of a Branching Process Conditioned on the Total Progeny
The maximum M of a critical Bienaymé-Galton-Watson process conditioned on the total progeny N is studied. Imbedding of the process in a random walk is used. A limit theorem for the distribution of M as N → ∞ is proved. The result is trasferred to the non-critical processes. A corollary for the maximal strata of a random rooted labeled tree is obtained.
On the maximum of a diffusion process in a drifted brownian environment
On the mean speed of convergence of empirical and occupation measures in Wasserstein distance
In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measures of ergodic Markov chains. One motivation is the approximation of a probability measure by finitely supported measures (the quantization problem). It is found that rates for empirical or occupation measures match or are close to previously known optimal quantization rates in several cases. This is notably...
On the measurement of the activity of a radioactive source and a related stochastic process.
A method is presented to compute the activity of a radioactive source. The principle of the method is based on the tuning of b, the time constant of the RC circuit of the detector with l being the rate of emission of the source, using a statistical argument.The stochastical process involved refers to the distribution of the following random voltage:Vt = ∑(0 < ti ≤ t) Yi c-b(t - ti)where the ti are Poisson dates of emission and the Yi are random or deterministic pulse heights. The case of...
On the M/G/1 retrial queue subjected to breakdowns
Retrial queueing systems are characterized by the requirement that customers finding the service area busy must join the retrial group and reapply for service at random intervals. This paper deals with the M/G/1 retrial queue subjected to breakdowns. We use its stochastic decomposition property to approximate the model performance in the case of general retrial times.
On the M/G/1 retrial queue subjected to breakdowns
Retrial queueing systems are characterized by the requirement that customers finding the service area busy must join the retrial group and reapply for service at random intervals. This paper deals with the M/G/1 retrial queue subjected to breakdowns. We use its stochastic decomposition property to approximate the model performance in the case of general retrial times.
On the micture of some sontinuous distributions
On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments
Let be the empirical distribution function (df) pertaining to independent random variables with continuous df . We investigate the minimizing point of the empirical process , where is another df which differs from . If and are locally Hölder-continuous of order at a point our main result states that converges in distribution. The limit variable is the almost sure unique minimizing point of a two-sided time-transformed homogeneous Poisson-process with a drift. The time-transformation...
On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments
Let Fn be the empirical distribution function (df) pertaining to independent random variables with continuous df F. We investigate the minimizing point of the empirical process Fn - F0, where F0 is another df which differs from F. If F and F0 are locally Hölder-continuous of order α at a point τ our main result states that converges in distribution. The limit variable is the almost sure unique minimizing point of a two-sided time-transformed homogeneous Poisson-process with a drift. The time-transformation...
On the mixed even-spin Sherrington–Kirkpatrick model with ferromagnetic interaction
We study a spin system with both mixed even-spin Sherrington–Kirkpatrick (SK) couplings and Curie–Weiss (CW) interaction. Our main results are: (i) The thermodynamic limit of the free energy is given by a variational formula involving the free energy of the SK model with a change in the external field. (ii) In the presence of a centered Gaussian external field, the positivity of the overlap and the extended Ghirlanda–Guerra identities hold on a dense subset of the temperature parameters. (iii) We...
On the mixed fractional Brownian motion.
On the Modality of Convex Polygons.