On the relationship between subordinate killed and killed subordinate processes.
On the relative lengths of excursions derived from a stable subordinator
On the remainder term of the de Moivre-Laplace formula.
On the Rényi dimension
On the Rényi theory of conditional probabilities
On the representation of solutions of stochastic differential equations
On the re-rooting invariance property of Lev́y trees.
On the robustness of properties characterizing the normal distribution
On the sample path behavior of the first passage time process of a brownian motion with drift
On the sample paths of diagonal brownian motions on the infinite dimensional torus
On the second-order correlation function of the characteristic polynomial of a real symmetric Wigner matrix.
On the self-intersection local time of Brownian motion via chaos expansion.
On the separately excessive functions. (Sur les fonctions séparément excessives.)
On the sequence of integer parts of a good sequence for the ergodic theorem
If is a sequence of real numbers which is good for the ergodic theorem, is the sequence of the integer parts good for the ergodic theorem ? The answer is negative for the mean ergodic theorem and affirmative for the pointwise ergodic theorem.
On the set of optimal controls for Markov chains with rewards
On the sharpened Heisenberg-Weyl inequality.
On the short time asymptotic of the stochastic Allen–Cahn equation
A description of the short time behavior of solutions of the Allen–Cahn equation with a smoothened additive noise is presented. The key result is that in the sharp interface limit solutions move according to motion by mean curvature with an additional stochastic forcing. This extends a similar result of Funaki [Acta Math. Sin (Engl. Ser.)15 (1999) 407–438] in spatial dimension n=2 to arbitrary dimensions.
On the shuffling algorithm for domino tilings.
On the singular limit of solutions to the Cox-Ingersoll-Ross interest rate model with stochastic volatility
In this paper we are interested in term structure models for pricing zero coupon bonds under rapidly oscillating stochastic volatility. We analyze solutions to the generalized Cox–Ingersoll–Ross two factors model describing clustering of interest rate volatilities. The main goal is to derive an asymptotic expansion of the bond price with respect to a singular parameter representing the fast scale for the stochastic volatility process. We derive the second order asymptotic expansion of a solution...
On the singular values of random matrices
We present an approach that allows one to bound the largest and smallest singular values of an random matrix with iid rows, distributed according to a measure on that is supported in a relatively small ball and linear functionals are uniformly bounded in for some , in a quantitative (non-asymptotic) fashion. Among the outcomes of this approach are optimal estimates of not only in the case of the above mentioned measure, but also when the measure is log-concave or when it a product measure...