Related papers: Duality relations between spatial birth-death proc…
We examine the role of boundaries and the structure of nontrivial duality functions for three non conservative interacting particle systems in one dimension that model epidemic spreading: (i) the diffusive contact process (DCP), (ii) a…
We discuss dual time evolution scenarios which, albeit running according to the same real time clock, in each considered case may be mapped among each other by means of an analytic continuation in time. This dynamical duality is a generic…
The hierarchies of evolution equations of classical many-particle systems are formulated as evolution equations in functional derivatives. In particular the BBGKY hierarchy for marginal distribution functions, the dual BBGKY hierarchy for…
This paper is devoted to the use of the entropy and duality methods for the existence theory of reaction-cross diffusion systems consisting of two equations, in any dimension of space. Those systems appear in population dynamics when the…
Population dynamics of individuals undergoing birth and death and diffusing by short or long ranged twodimensional spatial excursions (Gaussian jumps or L\'{e}vy flights) is studied. Competitive interactions are considered in a global case,…
Analogues of stepping--stone models are considered where the site--space is continuous, the migration process is a general Markov process, and the type--space is infinite. Such processes were defined in previous work of the second author by…
A Feller's Brownian motion is a diffusion process on the half-line with general boundary behavior at the origin, described by four parameters. A birth-death process, on the other hand, is a continuous-time Markov chain on the nonnegative…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
As a generic model for transport of interacting fermions through a barrier or interstitials in a lattice, quantum Brownian motion in a periodic potential is studied. There is a duality transformation between the continuous coordinate or…
A method to direct evaluation of expectations for Langevin systems (stochastic differential equations) is proposed. The method is based on a birth-death process which is derived using combinations of dummy variables and It{\^o} formula. As…
Weaving Hilbert space frames have been introduced recently by Bemrose et al. to deal with some problems in distributed signal processing. In this paper, we survey this topic from the viewpoint of the duality principle, so we obtain new…
Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for…
A form of time series path integral expansion is provided that enables both analytic and numerical temporal effect calculations for a range of stochastic processes. Birth-death processes with linear rates are analysed via coherent state…
Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript…
We present a derivation of the kinetic equation describing the secular evolution of spatially inhomogeneous systems with long-range interactions, the so-called inhomogeneous Landau equation, by relying on a functional integral formalism. We…
We provide a perturbative framework to calculate extreme events of non-Markovian processes, by mapping the stochastic process to a two-species reaction diffusion process in a Doi-Peliti field theory combined with the Martin-Siggia-Rose…
We construct a class of one-dimensional diffusion processes on the particles of branching Brownian motion that are symmetric with respect to the limits of random martingale measures. These measures are associated with the extended extremal…
This article introduces a novel construction of the two-dimensional fractional Brownian motion (2D fBm) with dependent components. Unlike similar models discussed in the literature, our approach uniquely accommodates the full range of model…
Individual-based models of chemical or biological dynamics usually consider individual entities diffusing in space and performing a birth-death type dynamics. In this work we study the properties of a model in this class where the birth…
A stochastic simulation algorithm for the computation of multitime correlation functions which is based on the quantum state diffusion model of open systems is developed. The crucial point of the proposed scheme is a suitable extension of…