相关论文: Bivariate Uniqueness and Endogeny for Recursive Di…

This paper has been withdrawn by the author(s), due an error in the proof.

We discuss several connections between discrete and continuous random trees. In the discrete setting, we focus on Galton-Watson trees under various conditionings. In particular, we present a simple approach to Aldous' theorem giving the…

This article has been withdrawn due to a mistake which is explained in version 2.

We discuss the nature of the two-stage percolation transition on the enhanced binary tree in order to explain the disagreement in the estimation of the second transition probability between the one in our recent paper (J. Phys. A:Math.…

Results have been moved to a published article, see arXiv:0812.2669v4[math.PR]

In this paper, we announce a rigorous approach to establishing uniqueness results, under certain conditions, for initial-boundary-value problems for a class of linear evolution partial differential equations (PDEs) formulated in a…

The Marked Binary Branching Tree (MBBT) is the family tree of a rate one binary branching process, on which points have been generated according to a rate one Poisson point process, with i.i.d. uniformly distributed activation times…

In this paper, we first prove existence and uniqueness of the solution of a backward doubly stochastic differential equation (BDSDE) and of the related stochastic partial differential equation (SPDE) under monotonicity assumption on the…

Existing work on Counterfactual Explanations (CE) and Algorithmic Recourse (AR) has largely focused on single individuals in a static environment: given some estimated model, the goal is to find valid counterfactuals for an individual…

Subdiffusive fractional equations are not structurally stable with respect to spatial perturbations to the anomalous exponent (Phys. Rev. E 85, 031132 (2012)). The question arises of applicability of these fractional equations to model real…

Linear regressions with endogeneity are widely used to estimate causal effects. This paper studies a framework that involves two common practical issues: endogeneity of the regressors and heteroskedasticity that depends on endogenous…

In certain problems in a variety of applied probability settings (from probabilistic analysis of algorithms to statistical physics), the central requirement is to solve a recursive distributional equation of the form X =^d…

This paper presents existence and uniqueness results for reflected backward doubly stochastic differential equations (in short RBDDSEs) in a convex domain D. Moreover, using a stochastic flow approach a probabilistic interpretation for a…

Bass and Pardoux (1987) deduce from the Krein-Rutman theorem a reverse ergodic theorem for a sub-probability transition function, which turns out to be a key tool in proving uniqueness of reflecting Brownian Motion in cones in Kwon and…

We consider a random process on recursive trees, with three types of events. Vertices give birth at a constant rate (growth), each edge may be removed independently (fragmentation of the tree) and clusters (or trees) are frozen with a rate…

With a view to numerical applications we address the following question: given an ergodic Brownian diffusion with a unique invariant distribution, what are the invariant distributions of the duplicated system consisting of two trajectories?…

We prove well-posedness results for backward stochastic differential equations (BSDEs) and reflected BSDEs with an optional obstacle process in the case of appropriately weighted $\mathbb{L}^2$-data when the generator is integrated with…

We obtain a number of new general properties, related to the closedness of the class of long-tailed distributions under convolutions, that are of interest themselves and may be applied in many models that deal with "plus" and/or "max"…

We revisit the model of the ballistic deposition studied in \cite{bdeposition} and prove several combinatorial properties of the random tree structure formed by the underlying stochastic process. Our results include limit theorems for the…

Robustness of two coupled networks system has been studied only for dependency coupling (S. Buldyrev et. al., Nature, 2010) and only for connectivity coupling (E. A. Leicht and R. M. D'Souza, arxiv:09070894). Here we study, using a…