Related papers: Trait evolution with jumps: illusionary normality
In this paper we consider a branching particle system consisting of particles moving according to the Ornstein-Uhlenbeck process in R^d and undergoing a binary, supercritical branching with a constant rate \lambda>0. This system is known to…
We develop here a stochastic framework for modeling and segmenting transient spindle-like oscillatory bursts in electroencephalogram (EEG) signals. At the modeling level, individual spindles are represented as path realizations of a…
We investigate the temporal evolution and spatial propagation of branching annihilating random walks in one dimension. Depending on the branching and annihilation rates, a few-particle initial state can evolve to a propagating finite…
We consider a stochastic process driven by a diffusion and jumps. We devise a technique, which is based on a discrete record of observations, for identifying the times when jumps larger than a suitably defined threshold occurred. The…
The dynamics of the avalanche width in the evolution model is described using a random walk picture. In this approach the critical exponents for avalanche distribution, $\tau$, and avalanche average time, $\gamma$, are found to be the same…
Branch-specific substitution models are popular for detecting evolutionary change-points, such as shifts in selective pressure. However, applying such models typically requires prior knowledge of change-point locations on the phylogeny or…
We consider the statistical motion of a convex rigid body in a gas of N smaller (spherical) atoms close to thermodynamic equilibrium. Because the rigid body is much bigger and heavier, it undergoes a lot of collisions leading to small…
In this paper, a branching process model of the Northern Spotted Owl is simulated. We focus on the time until extinction. It is shown how an approximation of the model with a multivariate autoregressive process works well near the…
We present a theoretical framework that enables investigating rare transitions in a general model of an active particle in an external potential, with the thermal Active Ornstein-Uhlenbeck Particle (AOUP) appearing as a special case. Using…
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes…
In this paper, we introduce a family of processes with values on the nonnegative integers that describes the dynamics of populations where individuals are allowed to have different types of interactions. The types of interactions that we…
Ageing's sensitivity to natural selection has long been discussed because of its apparent negative effect on individual's fitness. Thanks to the recently described (Smurf) 2-phase model of ageing we were allowed to propose a fresh angle for…
A deterministic walk in a random environment can be understood as a general random process with finite-range dependence that starts repeating a loop once it reaches a site it has visited before. Such process lacks the Markov property. We…
We investigate the distributional properties of two generalized Ornstein-Uhlenbeck (OU) processes whose stationary distributions are the gamma law and the bilateral gamma law, respectively. The said distributions turn out to be related to…
Under the effect of strong genetic drift, it is highly probable to observe gene fixation or gene loss in a population, shown by infinite peaks on a coherently constructed potential energy landscape. It is then important to ask what such…
We are interested in modeling Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions. The population is modeled as a stochastic point process whose generator captures…
Phylogenetic comparative methods correct for shared evolutionary history among a set of non-independent organisms by modeling sample traits as arising from a diffusion process along on the branches of a possibly unknown history. To…
Recent studies have demonstrated an interesting connection between the asymptotic behavior at ruin of a L\'evy insurance risk process under the Cram\'er-Lundberg and convolution equivalent conditions. For example, the limiting distributions…
Biological evolution in a sequence space with random fitnesses is studied within Eigen's quasispecies model. A strong selection limit is employed, in which the population resides at a single sequence at all times. Evolutionary trajectories…
It is generally accepted that the asset price processes contain jumps. In fact, pure jump models have been widely used to model asset prices and/or stochastic volatilities. The question is: is there any statistical evidence from the…