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We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the asset is driven by Browni ...
We investigate the superfluid-insulator quantum phase transition in a disordered one-dimensional Bose gas in the mean-field limit by studying the probability distribution of the density. The superfluid phase is characterized by a vanishing probability to h ...
Modern data storage systems are extremely large and consist of several tens or hundreds of nodes. In such systems, node failures are daily events, and safeguarding data from them poses a serious design challenge. The focus of this thesis is on the data rel ...
The excursion set theory, where density perturbations evolve stochastically with the smoothing scale, provides a method for computing the dark matter halo mass function. The computation of the mass function is mapped into the so-called first-passage time p ...
We design a sublinear Fourier sampling algorithm for a case of sparse off-grid frequency recovery. These are signals with the form f(t)=∑kj=1ajeiωjt+ν^ , t∈Z ; i.e., exponential polynomials with a noise term. The frequencies {ω j } satisfy ω j ∈ [η,2π − η ...
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 introduce contextual stochastic bilevel optimization (CSBO) -- a stochastic bilevel optimization framework with the lower-level problem minimizing an expectation conditioned on some contextual information and the upper-level decision variable. This fram ...
We address adaptive multivariate polynomial approximation by means of the discrete least-squares method with random evaluations, to approximate in the L2 probability sense a smooth function depending on a random variable distributed according to a given pr ...
We propose three modeling methods using a mobile sensor network to generate high spatio-temporal resolution air pollution maps for urban environments. In our deployment in Lausanne (Switzerland), dedicated sensing nodes are anchored to the public buses and ...
This thesis is devoted to the study of the effect of disorder on low-dimensional weakly interacting Bose gases. In particular, the disorder triggers a quantum phase transition in one dimension at zero temperature that is investigated here through the study ...
