Related papers: A Generic Approach to Solving Jump Diffusion Equat…
We consider a trait-structured population subject to mutation, birth and competition of logistic type, where the number of coexisting types may fluctuate. Applying a limit of rare mutations to this population while keeping the population…
We consider a Markov process on a Riemannian manifold, which solves a stochastic differential equation in the interior of the manifold and jumps according to a deterministic reset map when it reaches the boundary. We derive a partial…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
The unified description of diffusion processes that cross over from a ballistic behavior at short times to normal or anomalous diffusion (sub- or superdiffusion) at longer times is constructed on the basis of a non-Markovian generalization…
We present a novel method for solving population density equations (PDEs), where the populations can be subject to non-Markov noise for arbitrary distributions of jump sizes. The method combines recent developments in two different…
This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master…
Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or…
The nonlocal Fisher equation is a diffusion-reaction equation with a nonlocal quadratic competition, which describes the reaction between distant individuals. This equation arises in evolutionary biological systems, where the arena for the…
Reaction diffusion equations have been used to model a wide range of biological phenomenon related to population spread and proliferation from ecology to cancer. It is commonly assumed that individuals in a population have homogeneous…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a…
By discretising space into compartments and letting system dynamics be governed by the reaction-diffusion master equation, it is possible to derive and simulate a stochastic model of reaction and diffusion on an arbitrary domain. However,…
We present a generalized linear response theory for mixed jump-diffusion models -- combining Gaussian and L\'evy noise interacting with nonlinear dynamics -- by deriving comprehensive response formulas accounting for perturbations to both…
We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…
This paper is devoted the the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations…
Aim of this note is to analyse branching Brownian motion within the class of models introduced in the recent paper [4] and called chemical diffusion master equations. These models provide a description for the probabilistic evolution of…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
We present a novel simulation-free framework for training continuous-time diffusion processes over very general objective functions. Existing methods typically involve either prescribing the optimal diffusion process -- which only works for…
This paper establishes limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamic coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump…
Decision-making in dynamic environments typically requires adaptive evidence accumulation that weights new evidence more heavily than old observations. Recent experimental studies of dynamic decision tasks require subjects to make decisions…