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This paper derives a unifying theorem establishing consistency results for a broad class of tree-based algorithms. It improves current results in two aspects. First of all, it can be applied to algorithms that vary from traditional Random…
This paper presents a model of asymmetric bifurcating autoregressive process with random coefficients. We couple this model with a Galton Watson tree to take into account possibly missing observations. We propose least-squares estimators…
We prove existence and uniqueness of the reflected backward stochastic differential equation's (RBSDE) solution with a lower obstacle which is assumed to be right upper-semicontinuous but not necessarily right-continuous in a filtration…
In this paper, an optimal switching problem is proposed for one-dimensional reflected backward stochastic differential equations (RBSDEs, for short) where the generators, the terminal values and the barriers are all switched with positive…
In [Ald00], Aldous investigates a symmetric Markov chain on cladograms and gives bounds on its mixing and relaxation times. The latter bound was sharpened in [Sch02]. In the present paper we encode cladograms as binary, algebraic measure…
In this paper, we develop a general methodology to prove weak uniqueness for stochastic differential equations with coefficients depending on some path-functionals of the process. As an extension of the technique developed by Bass \&…
Here we define and study the properties of retrodictive inference. We derive equations relating retrodiction entropy and thermodynamic entropy, and as a special case, show that under equilibrium conditions, the two are identical. We…
The paper studies a PDE model for the growth of a tree stem or a vine, having the form of a differential inclusion with state constraints. The equations describe the elongation due to cell growth, and the response to gravity and to external…
In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…
Although the third law of thermodynamics was established almost a century ago, it is not yet universally considered to be a fundamental law of physics. A major problem is that there are many materials having residual entropy. Amorphous…
Reversible systems exhibit both forward computations and backward computations, where the aim of the latter is to undo the effects of the former. Such systems can be compared via forward-reverse bisimilarity as well as its two components,…
This article deals with directional rotational deviations for non-wandering periodic point free homeomorphisms of the 2-torus which are homotopic to the identity. We prove that under mild assumptions, such a homeomorphism exhibits uniformly…
Consider a uniformly sampled random $d$-regular graph on $n$ vertices. If $d$ is fixed and $n$ goes to $\infty$ then we can relate typical (large probability) properties of such random graph to a family of invariant random processes (called…
The article is withdrawn since we decided not to publish it in the present form but to divide it in two parts. One of these parts concerns the mathematical aspects of Return Radius calculation and the rewritten article is already available…
We introduce a persistent random walk model with finite velocity and self-reinforcing directionality, which explains how exponentially distributed runs self-organize into truncated L\'evy walks observed in active intracellular transport by…
Molecular phylogenetic techniques do not generally account for such common evolutionary events as site insertions and deletions (known as indels). Instead tree building algorithms and ancestral state inference procedures typically rely on…
Since the celebrated paper by El Karoui, Peng and Quenez [Mathematical Finance, 7 (1997), 1--71], backward stochastic differential equations have found wide applications in stochastic control, financial technology and machine learning. In…
The Aldous diffusion is a conjectured Markov process on the space of real trees that is the continuum analogue of discrete Markov chains on binary trees. We construct this conjectured process via a consistent system of stationary evolutions…
This work addresses the problem of uniquely determining a rotational motion from continuous time-dependent measurements within the frameworks of parallel-beam and diffraction tomography. The motivation stems from the challenge of imaging…
Inspired by an example of Grebogi et al [1], we study a class of model systems which exhibit the full two-step scenario for the nonautonomous Hopf bifurcation, as proposed by Arnold [2]. The specific structure of these models allows a…