Stopping Lines Research Articles

Efficacité, maintien thérapeutique et motifs d’arrêt du tocilizumab (TCZ) : étude monocentrique et rétrospective chez 88 patients suivis pour une polyarthrite rhumatoïde (PR) au CHU de Reims

Study the therapeutic maintenance, efficacy and reasons for tocilizumab stop in daily practice. A monocentric, retrospective study of patients treated for rheumatoid arthritis who received at least one TCZ infusion between January2009 and December2015. Therapeutic maintenance was evaluated using the Kaplan-Meier method. The efficacy of TCZ was measured by DAS28 and the EULAR response. Reasons for stopping and new treatment lines were also collected. Of the 88patients (83% women and 17% men) who were included, the mean age was 54±12.5years. There were 75% positive rheumatoid factors and 76% positive anti-CCP. The mean duration of the follow-up was 31months. TCZ was used as monotherapy in 24patients (27%). Before the introduction of TCZ, the mean DAS28 was 5.07±1.32. The EULAR response at 1year in patients still under treatment (n=63) was obtained in 59(93.7%) patients, 46good responders and 13moderate responders. Therapeutic maintenance was 82.9%, 72.5%, 68.7% and 57.2%, respectively, at 12, 24, 36 and 54months. Twenty-eight patients (32%) followed TCZ, 10 for adverse events and 14 for ineffectiveness. Abatacept was the main new therapeutic line. The therapeutic maintenance of TCZ in common practice over a long period of follow-up is similar to pivotal studies. Efficacy data are reassuring in the long-term.

Assessing the performance of a charge‐while‐driving system in urban arterial roads: insight from a microsimulation model

This study presents a method based on traffic microsimulation to support feasibility studies on charge-while-driving (CWD) systems for fully electric vehicles in urban environments. The examined CWD solution is deployed by charging zones (CZs), which are installed before the stopping lines at signalised intersections. The opportunity to charge an electric vehicle en route is provided for almost stationary vehicle conditions, when it may be in queue for junction control requirements. The analysed scenario refers to a 2 km urban arterial with eight signalised intersections, where 10% of the traffic is assumed to be electric vehicles. CWD performance results are reported from the viewpoints of both driver and energy provider. The estimated stop time for electric vehicles at any section can vary and is often below 30 s. However, the entire stop time for a vehicle along the arterial is higher: ∼50% of the vehicles can charge in a range of 10–65 s. For the energy operator's viewpoint, a support analysis for the CZ location was performed by observing the charging opportunities at various sections. Finally, the total electric power provided for the entire system is estimated.

Extremes in Branching Random Walk and Branching Brownian Motion

Branching random walk (BRW) and branching Brownian motion (BBM) are mathematical models for population growth and spatial displacement. When resources are plentiful, population sizes grow exponentially in time. In such a situation, exceptional (or extreme) individuals will be found far from the bulk of the population. The study of such individuals, and their ancestral lineages, was the subject of the workshop. On one hand, this is a classical topic, with well-known connections to the KPP-equation and to search algorithms. On the other hand, substantial recent developments have recently been obtained via new approaches to the subject (stopping lines and spines, the view from the tip, multivariate analytic combinatorics), or from researchers working in seemingly distinct areas (from stochastic partial differential equations to theoretical physics).

Supercritical super-Brownian motion with a general branching mechanism and travelling waves

Nous proposons une approche probabiliste au problème classique de l’existence, de l’unicité et du comportement asymptotique des solutions monotones de l’équation de propagation de front associée à l’équation parabolique du super-mouvement brownien de mécanisme de branchement général. Bien que largement inspiré par l’approche de Kyprianou (Ann. Inst. Henri Poincaré Probab. Stat. 40 (2004) 53–72) pour le mouvement brownien branchant, cet article ouvre plusieurs perspectives nouvelles. Notre analyse inclut le rôle de la normalisation de Seneta–Heyde qui, dans cette situation, s’inspire du travail classique de Grey (J. Appl. Probab. 11 (1974) 669–677). Nous donnons une explication trajectorielle de la décomposition en épine (la particule immortelle d’Evans), en utilisant la $\mathbb{N}$-mesure de Dynkin–Kuznetsov comme ingrédient clef. En outre, dans l’esprit des lignes d’arrêt de Neveu nous utilisons à plusieurs reprises les mesures de sortie de Dynkin. La nature générale du mécanisme de branchement rend l’analyse du problème plus délicate et nous proposons une dichotomie exacte basée sur un moment $X(\log X)^{2}$ pour la convergence presque-sûre de la martingale dérivée (pour la valeur critique de son paramètre) vers une limite non-triviale. Ceci diffère du cas du mouvement brownien branchant (Ann. Inst. Henri Poincaré Probab. Stat. 40 (2004) 53–72) et de la marche aléatoire branchante (Adv. in Appl. Probab. 36 (2004) 544–581), où un écart dans les hypothèses sur les moments apparaît entre les conditions nécessaires et suffisantes. Notre approche probabiliste permet de retrouver des résultats connus d’existence, d’unicité et de comportement asymptotique pour l’équation de propagation de front reliée au super-mouvement brownien.

An optimal stopping problem for fragmentation processes

In this article we consider a toy example of an optimal stopping problem driven by fragmentation processes. We show that one can work with the concept of stopping lines to formulate the notion of an optimal stopping problem and moreover, to reduce it to a classical optimal stopping problem for a generalized Ornstein–Uhlenbeck process associated with Bertoin’s tagged fragment. We go on to solve the latter using a classical verification technique thanks to the application of aspects of the modern theory of integrated exponential Lévy processes.

A Notion of Stopping Line for Set-Indexed Processes

In this paper, we introduce the class of $$\mathcal {A}$$ -stopping lines which generalize the planar stopping lines in Merzbach [(1980), Stochastic Process. Appl. 10, 49–63] by replacing the positive quadrant of the plane by a collection $$\mathcal {A}$$ of compact subsets of a fixed topological space. Our notion of stopping line also compliments and generalizes the stopping sets defined in Ivanoff and Merzbach [(1995), Stochastic Process. Appl. 57, 83–98].

Martingale convergence and the stopped branching random walk

We discuss the construction of stopping lines in the branching random walk and thus the existence of a class of supermartingales indexed by sequences of stopping lines. Applying a method of Lyons (1997) and Lyons, Pemantle and Peres (1995) concerning size biased branching trees, we establish a relationship between stopping lines and certain stopping times. Consequently we develop conditions under which these supermartingales are also martingales. Further we prove a generalization of Biggins' Martingale Convergence Theorem, Biggins (1977a) within this context.

A note on branching Lévy processes

We show for the branching Lévy process that it is possible to construct two classes of multiplicative martingales using stopping lines and solutions to one of two source equations. The first class, similar to those martingales of Chauvin (1991, Ann. Probab. 30, 1195–1205) and Neveu (1988, Seminar on Stochastic Processes 1987, Progress in Probability and Statistics, vol. 15, Birkhaüser, Boston, pp. 223–241) have a source equation which provides travelling wave solutions to a generalized version of the K-P-P equation. For the second class of martingales, similar to those of Biggins and Kyprianou (1997, Ann. Probab. 25, 337–360), the source equation is a functional equation. We show further that under reasonably broad circumstances, these equations share the same solutions and hence the two types of martingales are one and the same. This conclusion also tells us something more about the nature of the solutions to the first of our two equations.

Characterization of the spatial poisson process by stopping lines*

A way of studying a two-parameter point process by reducing it to a one-parameter point process is given. We prove the following characterization of a planar Poisson process: a two-parameter point process N is a non-homogeneous Poisson process adapted to its filtration, if and only if it is a one-parameter doubly stochastic Poisson process at any increasing and continuous family of stopping lines dependent on the initial conditions

On right continuity of a family of two-parameter σ-fields

This paper first proves a sufficient and necessary condition for the right continuity of a family of two-parameter σ-fields. Then, it proceeds to introduce condition ( F s 3) and proves that condition ( F s 3) is equivalent to right continuity of a family of σ-fields prior to stopping lines.

Product Martingales and Stopping Lines for Branching Brownian Motion

For a branching Brownian motion, a probability space of trees is defined. By analogy with stopping times on $\mathbb{R}$, stopping lines are defined to get a general branching property. We exhibit an intrinsic class of martingales which are products indexed by the elements of a stopping line. We prove that all these martingales have the same limit which we identify. Two particular cases arise: the line of particles living at time $t$ and the first crossings of a straight line whose equation is $y = at - x$ in the plane $(y,t)$.

Markov Properties for Point Processes on the Plane

It is proved that for a wide class of point processes indexed by the positive quadrant of the plane, and for a class of compact sets in this quadrant, the germ $\sigma$-field is equal to the $\sigma$-field generated by the values of the process on the set. Therefore, there exists a large family of point processes in the plane (and among them the spatial Poisson process) which satisfy the sharp Markov property in the sense of P. Levy. The strong Markov property with respect to stopping lines is also studied. Some examples are obtained by taking transformations of the probability measure.

A Martingale Approach to Point Processes in the Plane

A rigorous definition of two-parameter point processes is given as a distribution of a denumerable number of random points in the plane. A characterization with stopping lines and relation with predictability are obtained. Using the one-parameter multivariate point-process representation, a general representation theorem for a wide class of martingales is presented, which extends the representation theorem with respect to a Poisson process.

A Characterization of the Spatial Poisson Process and Changing Time

Watanabe proved that if $X_t$ is a point process such that $X_t - t$ is a martingale, then $X_t$ is a Poisson process and this result was generalized by Bremaud for doubly stochastic Poisson processes. Here we define two-parameter point processes and extend this property without needing the strong martingale condition. Using this characterization, we study the problem of transforming a two-parameter point process into a two-parameter Poisson process by means of a family of stopping lines as a time change. Nualart and Sanz gave conditions in order to transform a square integrable strong martingale into a Wiener process. Here, we do the same for the Poisson process by a similar method but under more general conditions.

Filtrations for the two parameter jump process

A process which has just one jump, and whose time parameter is the positive quadrant [0, ∞] × [0, ∞], is considered. Following Merzbach, related stopping lines are introduced, and the filtration { F t 1, t 2 3} considered in this paper is such that, modulo completion, the σ-field F t 1, t 2 3 is the Borel field on the region L t1,t2={(s 1,s 2); 0⩽s 1⩽t 1 or0⩽s 2⩽t 2} , together with the atom which is the complement in Ω = [0, ∞] 2 of L t 1, t 2 . Optional and predictable projections of related processes are defined, together with their dual projections, and an integral representation for martingales is obtained.

The conditional independence property in filtrations associated to stopping lines

The conditional independence property in filtrations associated to stopping lines

Stopping for two-dimensional stochastic processes

The aim of this paper is to introduce some techniques that can be used in the study of stochastic processes which have as parameter set the positive quadrant of the plane R 2 +. We define stopping lines and derive an interesting property of measurability for them. The notion of predictability is developed, and we show the connection between predictable processes, fields associated with stopping lines, and predictable stopping lines. We also give a theorem of section for predictable sets. Extension to processes indexed by any partially ordered set with some regularity assumptions can be carried out quite easily with the same techniques.