The goal of this paper is to provide a wavelet series representation for Linear Multifractional Stable Motion (LMSM). Instead of using Daubechies wavelets, which are not given in closed form, we use a Haar wavelet, thus yielding a more explicit expression than that in Ayache and Hamonier (in press).

We consider the stochastic wave equation on the real line driven by space–time white noise and with irregular initial data. We give bounds on higher moments and, for the hyperbolic Anderson model, explicit formulas for second moments. These bounds imply weak intermittency and allow us to...

We examine symmetric extensions of symmetric Markov processes with one boundary point. Relationship among various normalizations of local times, entrance laws and excursion laws is studied. Dirichlet form characterization of elastic one-point reflection of symmetric Markov processes is derived....

In this paper, we establish a central limit theorem for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfying a second moment condition. This central limit theorem generalizes and unifies all the central limit theorems obtained recently in...

We study the problem of existence, uniqueness and approximation of solutions of finite dimensional Stratonovich stochastic differential equations with reflecting boundary condition driven by semimartingales with jumps. As an application we generalize known results on the Wong–Zakai type...

We obtain central limit theorems for additive functionals of stationary fields under integrability conditions on the higher-order spectral densities. The proofs are based on the Hölder–Young–Brascamp–Lieb inequality.

We study the optimal stopping problem of pricing an American Put option on a Zero Coupon Bond (ZCB) in Musiela’s parametrization of the Heath–Jarrow–Morton (HJM) model for forward interest rates.

The estimation of local characteristics of Itô semimartingales has received a great deal of attention in both academia and industry over the past decades. In various papers limit theorems were derived for functionals of increments and ranges in the infill asymptotics setting. In this paper we...

The Multifractal Embedded Branching Process (MEBP) process and Canonical Embedded Branching Process (CEBP) process were introduced by Decrouez and Jones (2012). The CEBP is a process in which the crossings of dyadic intervals constitute a branching process. An MEBP process is defined as a...

We study the pruning process developed by Abraham and Delmas (2012) on the discrete Galton–Watson sub-trees of the Lévy tree which are obtained by considering the minimal sub-tree connecting the root and leaves chosen uniformly at rate λ, see Duquesne and Le Gall (2002). The tree-valued...