Concept
Wiener process
Related publications (102)
An extension of the stochastic sewing lemma and applications to fractional stochastic calculus
We give an extension of Le's stochastic sewing lemma. The stochastic sewing lemma proves convergence in of Riemann type sums for an adapted two-parameter stochastic process A, under certain conditions on the moments o ...
Cambridge Univ Press2024Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective
Victor Panaretos, Neda Mohammadi Jouzdani
We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...
Amsterdam2023CONVERGENCE AND NONCONVERGENCE OF SCALED SELF-INTERACTING RANDOM WALKS TO BROWNIAN MOTION PERTURBED AT EXTREMA
We use generalized Ray-Knight theorems, introduced by B. Toth in 1996, together with techniques developed for excited random walks as main tools for establishing positive and negative results concerning convergence of some classes of diffusively scaled sel ...
Cleveland2023Estimation of Self-Exciting Point Processes from Time-Censored Data
Thomas Alois Weber, Philipp Schneider
Self-exciting point processes, widely used to model arrival phenomena in nature and society, are often difficult to identify. The estimation becomes even more challenging when arrivals are recorded only as bin counts on a finite partition of the observatio ...
2023On a Finite-Size Neuronal Population Equation
Tilo Schwalger, Valentin Marc Schmutz, Eva Löcherbach
Population equations for infinitely large networks of spiking neurons have a long tradition in theoret-ical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form of a nonlinear ...
SIAM PUBLICATIONS2023Intrinsic area near the origin for self-similar growth-fragmentations and related random surfaces
We study the behaviour of a natural measure defined on the leaves of the genealogical tree of some branching processes, namely self-similar growth-fragmentation processes. Each particle, or cell, is attributed a positive mass that evolves in continuous tim ...
2022A driven tagged particle in asymmetric exclusion processes
We consider the asymmetric exclusion process with a driven tagged particle on Z which has different jump rates from other particles. When the non-tagged particles have non-nearest-neighbor jump rates , we show that the tagged particle can have a speed whic ...
INST MATHEMATICAL STATISTICS-IMS2022The Hausdorff measure of the range and level sets of Gaussian random fields with sectorial local nondeterminism
We determine the exact Hausdorff measure functions for the range and level sets of a class of Gaussian random fields satisfying sectorial local nondeterminism and other assumptions. We also establish a Chung-type law of the iterated logarithm. The results ...
INT STATISTICAL INST2022Skew-Brownian motion and pricing European exchange options br
This article derives a closed-form pricing formula for European exchange options under a non-Gaussianframework for the underlying assets, intending to resolve mispricing associated with a geometric Brownianmotion. The dynamics of each of the two correlated ...
ELSEVIER SCIENCE INC2022