Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

Lévy processes and infinitely divisible distributions

Real and Complex Analysis

Diffusion processes and their sample paths

The principal aim of this chapter is to familiarize the reader with the fact that the conditional distribution of the signal can be viewed as a stochastic process with values in the space of probability measures. While it is true that this chapter sets the scene for the subsequent chapters, it can be skipped by those readers whose interests are biased towards the applied aspects of the subject. The gist of the chapter can be summarized by the following.

The Stochastic Process π

Capturability analysis of the linear inverted pendulum (LIP) model enabled walking with constrained height based on the capture point . In this paper, we generalize this analysis to the variable-height inverted pendulum (VHIP) and show how it enables 3-D walking over uneven terrains based on capture inputs . Thanks to a tailored optimization scheme, we can compute these inputs fast enough for real-time model predictive control. We implement this approach as open-source software and demonstrate it in dynamic simulations.

https://hal.archives-ouvertes.fr/hal-01689331/document

Capturability-Based Pattern Generation for Walking With Variable Height

In this article, we study a branching random walk in an environment which depends on the time. This time-inhomogeneous environment consists of a sequence of macroscopic time intervals, in each of which the law of reproduction remains constant. We prove that the asymptotic behaviour of the maximal displacement in this process consists of a first ballistic order, given by the solution of an optimization problem under constraints, a negative logarithmic correction, plus stochastically bounded fluctuations.

/pdf/maximal-displacement-in-a-branching-random-walk-through-xh3z8dp0j1.pdf

Maximal displacement in a branching random walk through interfaces

Maximal displacement of a branching random walk in time-inhomogeneous environment

We propose an analysis and applications of sample pooling to the epidemiologic monitoring of COVID-19. We first introduce a model of the RT-qPCR process used to test for the presence of virus in a sample and construct a statistical model for the viral load in a typical infected individual inspired by large-scale clinical datasets. We present an application of group testing for the prevention of epidemic outbreak in closed connected communities. We then propose a method for the measure of the prevalence in a population taking into account the increased number of false negatives associated with the group testing method.

/pdf/group-testing-as-a-strategy-for-covid-19-epidemiological-4kado3yt0d.pdf

Group testing as a strategy for COVID-19 epidemiological monitoring and community surveillance.

Developments for 3D control of the center of mass (CoM) of biped robots are currently located in two local minima: on the one hand, methods that allow CoM height variations but only work in the 2D sagittal plane; on the other hand, nonconvex direct transcriptions of centroidal dynamics that are delicate to handle. This paper presents an alternative that controls the CoM in 3D via an indirect transcription that is both low-dimensional and solvable fast enough for real-time control. The key to this development is the notion of boundedness condition, which quantifies the capturability of 3D CoM trajectories.

https://hal.archives-ouvertes.fr/hal-01590509/document

Bastien Mallein

Papers

Capturability-Based Pattern Generation for Walking With Variable Height

Maximal displacement in a branching random walk through interfaces

Maximal displacement of a branching random walk in time-inhomogeneous environment

Group testing as a strategy for COVID-19 epidemiological monitoring and community surveillance.

Balance Control Using Both ZMP and COM Height Variations: A Convex Boundedness Approach