Related papers: Evolution equations for a cubic stochastic process
Stochastic invariant manifolds are crucial in modelling the dynamical behavior of dynamical systems under uncertainty. Under the assumption of exponential trichotomy, existence and smoothness of center manifolds for a class of stochastic…
Stellar evolution computations provide the foundation of several methods applied to study the evolutionary properties of stars and stellar populations, both Galactic and extragalactic. The accuracy of the results obtained with these…
We provide a detailed derivation of the Karhunen-Lo\`eve expansion of a stochastic process. We also discuss briefly Gaussian processes, and provide a simple numerical study for the purpose of illustration.
Evolutionary game dynamics describes the spreading of successful strategies in a population of reproducing individuals. Typically, the microscopic definition of strategy spreading is stochastic, such that the dynamics becomes deterministic…
Two integrable systems are constructed in a 2 + 1-dimensional space. Every of these systems involve two evolutions with negative numbers.
The evolution of complexity has been a central theme for Biology [2] and Artificial Life research [1]. It is generally agreed that complexity has increased in our universe, giving way to life, multi-cellularity, societies, and systems of…
The rigorous approach to the description of the kinetic evolution of a many-particle system composed of a trace hard sphere and an environment of finitely many hard spheres is developed. We prove that the evolution of states of a trace hard…
Several simple approximations for the evolution during the nucleation period have been presented. All of them have been compared with precise numerical solution and the errors have been estimated. All relative errors are enough small.
We begin by reviewing a technique to approximate the dynamics of stochastic programs --written in a stochastic process algebra-- by a hybrid system, suitable to capture a mixed discrete/continuous evolution. In a nutshell, the discrete…
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two…
In this review, we summarize recent developments in stochastic evolutionary game dynamics of finite populations.
Evolution by natural selection can be seen an algorithm for generating creative solutions to difficult problems. More precisely, evolution by natural selection is a class of algorithms that share a set of properties. The question we address…
In this paper, we consider an equation on random variables which can be reduced to the equation which describes the evolution of systems of fermions. We give some results of well-posedness for this equation on the spheres and torus of…
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…
Stochastic evolution underpins several approaches to the dynamics of open quantum systems, such as random modulation of Hamiltonian parameters, the stochastic Schrodinger equation (SSE), and the stochastic Liouville equation (SLE). These…
In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is…
The large amount of data on galaxies, up to higher and higher redshifts, asks for sophisticated statistical approaches to build adequate classifications. Multivariate cluster analyses, that compare objects for their global similarities, are…
We introduce the notion of a quasistatic dynamical system, which generalizes that of an ordinary dynamical system. Quasistatic dynamical systems are inspired by the namesake processes in thermodynamics, which are idealized processes where…
Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for…
Space-time fractional evolution equations are a powerful tool to model diffusion displaying space-time heterogeneity. We prove existence, uniqueness and stochastic representation of classical solutions for an extension of Caputo evolution…