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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 ...
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 ...
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 ...
This thesis consists of three applications of machine learning techniques to empirical asset pricing.In the first part, which is co-authored work with Oksana Bashchenko, we develop a new method that detects jumps nonparametrically in financial time series ...
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 ...
In a groundbreaking work, Duplantier, Miller and Sheffield showed that subcritical Liouville quantum gravity (LQG) coupled with Schramm-Loewner evolutions (SLE) can be obtained by gluing together a pair of Brownian motions. In this paper, we study the coun ...
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 ...
In this paper, we focus on isotropic and stationary sphere-cross-time random fields. We first introduce the class of spherical functional autoregressive-moving average processes (SPHARMA), which extend in a natural way the spherical functional autoregressi ...
We give an extension of Le's stochastic sewing lemma. The stochastic sewing lemma proves convergence in Lm of Riemann type sums ∑[s,t]∈πAs,t for an adapted two-parameter stochastic process A, under certain conditions on the moments o ...
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 ...
