Related papers: A sustainability condition for stochastic forest m…
We investigate conditioning Galton-Watson trees on general recursive-type events, such as the event that the tree survives until a specific level. It turns out that the conditioned tree is again a type of Galton-Watson tree, with different…
We provide a new approach for proving the indistinguishability of connected components of random one-or-two-ended oriented forests on unimodular random graphs. In particular, this approach leads to a new and simpler proof for the wired…
Random Forests have been extensively used in regression and classification, inspiring the development of various forest-based methods. Among these, Mondrian Forests, derived from the Mondrian process, mark a significant advancement.…
Random forests are an ensemble method relevant for many problems, such as regression or classification. They are popular due to their good predictive performance (compared to, e.g., decision trees) requiring only minimal tuning of…
In this paper, a new decay estimate for a class of stochastic evolution equations with weakly dissipative drifts is established, which directly implies the uniqueness of invariant measures for the corresponding transition semigroups.…
This paper explores a stochastic Gause predator-prey model with bounded or sub-linear functional response. The model, described by a system of stochastic differential equations, captures the influence of stochastic fluctuations on…
Machine learning models deployed in real-world settings must operate under evolving data distributions and constrained computational resources. This challenge is particularly acute in non-stationary domains such as energy time series,…
This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental…
Estimating phylogenetic trees is an important problem in evolutionary biology, environmental policy and medicine. Although trees are estimated, their uncertainties are discarded by mathematicians working in tree space. Here we explicitly…
Recent studies have adopted an approach of selecting accurate and diverse trees based on individual or collective performance within an ensemble for classification and regression problems. This work follows in the wake of these…
Random-cluster measures on infinite regular trees are studied in conjunction with a general type of `boundary condition', namely an equivalence relation on the set of infinite paths of the tree. The uniqueness and non-uniqueness of…
Plant survival is a key factor in forest dynamics and survival probabilities often vary across life stages. Studies specifically aimed at assessing tree survival are unusual and so data initially designed for other purposes often need to be…
Plant biomass estimation is critical due to the variability of different environmental factors and crop management practices associated with it. The assessment is largely impacted by the accurate prediction of different environmental…
We construct a model in which the tree property holds in $\aleph_{\omega + 1}$ and it is destructible under $\text{Col}(\omega, \omega_1)$. On the other hand we discuss some cases in which the tree property is indestructible under small or…
This paper investigates asymptotic behavior of a stochastic SIR epidemic model, which is a system with degenerate diffusion. It gives sufficient conditions that are very close to the necessary conditions for the permanence. In addition,…
We develop a novel continuous-time asymptotic framework for inference on whether the predictive ability of a given forecast model remains stable over time. We formally define forecast instability from the economic forecaster's perspective…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
We consider a class of parabolic stochastic partial differential equations featuring an antimonotone nonlinearity. The existence of unique maximal and minimal variational solutions is proved via a fixed-point argument for nondecreasing…
This paper introduces a novel nonparametric method for estimating high-dimensional dynamic covariance matrices with multiple conditioning covariates, leveraging random forests and supported by robust theoretical guarantees. Unlike…
We consider backward stochastic differential equations (BSDE) with nonlinear generators typically of quadratic growth in the control variable. A measure solution of such a BSDE will be understood as a probability measure under which the…