Evolution equations and diffusion operators for demographic dynamics

2019 ◽  
pp. 1-16
Author(s):  
Sheng-Ya Feng ◽  
Der-Chen Chang
Keyword(s):  
Evolution Equations ◽  
Demographic Dynamics ◽  
And Diffusion

scholarly journals Generalized Lemaítre–Tolman–Bondi spacetime under the influence of electric charge and Palatini f(R) gravity

2021 ◽  
Vol 81 (9) ◽  
Author(s):  
M. Z. Bhatti ◽  
Z. Yousaf ◽  
F. Hussain
Keyword(s):  
Electromagnetic Field ◽  
Evolution Equations ◽  
Mass Function ◽  
Diffusion Approximations ◽  
Riemann Curvature ◽  
Field Equations ◽  
Riemann Curvature Tensor ◽  
Inhomogeneous Universe ◽  
Dust Fluid ◽  
And Diffusion

AbstractThe objective of this article is to investigate the effects of electromagnetic field on the generalization of Lemaître–Tolman–Bondi (LTB) spacetime by keeping in view the Palatini f(R) gravity and dissipative dust fluid. For performing this analysis, we followed the strategy deployed by Herrera et al. (Phys Rev D 82(2):024021, 2010). We have explored the modified field equations along with kinematical quantities and mass function and constructed the evolution equations to study the dynamics of inhomogeneous universe along with Raychauduary and Ellis equations. We have developed the relation for Palatini f(R) scalar functions by splitting the Riemann curvature tensor orthogonally and associated them with metric coefficients using modified field equations. We have formulated these scalar functions for LTB and its generalized version, i.e., GLTB under the influence of charge. The properties of GLTB spacetime are consistent with those of the LTB geometry and the scalar functions found in both cases are comparable in the presence of charge and Palatini f(R) curvature terms. The symmetric properties of generalized LTB spacetime are also studied using streaming out and diffusion approximations.

scholarly journals On Jumps Stochastic Evolution Equations With Application of Homogenization and Large Deviations

2019 ◽  
Vol 11 (2) ◽  
pp. 125
Author(s):  
Cl´ement Manga ◽  
Alioune Coulibaly ◽  
Alassane Diedhiou
Keyword(s):  
Evolution Equation ◽  
Large Deviations ◽  
Evolution Equations ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Large Deviations Principle ◽  
Viscosity Parameter ◽  
Two Parameters ◽  
And Diffusion

We consider a class of jumps and diffusion stochastic differential equations which are perturbed by to two parameters:  ε (viscosity parameter) and δ (homogenization parameter) both tending to zero. We analyse the problem taking into account the combinatorial effects of the two parameters  ε and δ . We prove a Large Deviations Principle estimate for jumps stochastic evolution equation in case that homogenization dominates.

scholarly journals Diffusion Processes Satisfying a Conservation Law Constraint

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
J. Bakosi ◽  
J. R. Ristorcelli
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Conservation Law ◽  
Evolution Equations ◽  
Diffusion Processes ◽  
Random Variables ◽  
Planck Equation ◽  
Equation Model ◽  
First Four Moments ◽  
And Diffusion

We investigate coupled stochastic differential equations governing N nonnegative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires a set of fluctuating variables to be nonnegative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the nonnegativity and the unit-sum conservation law constraints are satisfied as the variables evolve in time. We investigate the consequences of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.

scholarly journals Completely monotone multinomial mittag-leffler type functions and diffusion equations with multiple time-derivatives

2021 ◽  
Vol 24 (1) ◽  
pp. 88-111
Author(s):  
Emilia Bazhlekova
Keyword(s):  
Laplace Transform ◽  
Evolution Equations ◽  
Diffusion Equations ◽  
Multiple Time ◽  
Fractional Evolution Equations ◽  
Relaxation Functions ◽  
Completely Monotone ◽  
Main Emphasis ◽  
And Diffusion ◽  
Modified Forms

Abstract The multinomial Mittag-Leffler function plays a crucial role in the study of multi-term time-fractional evolution equations. In this work we establish basic properties of the Prabhakar type generalization of this function with the main emphasis on complete monotonicity. As particular examples, the relaxation functions for equations with multiple time-derivatives in the so-called “natural” and “modified” forms are studied in detail and useful estimates are derived. The obtained results extend known properties of the classical Mittag-Leffler function. The main tools used in this work are Laplace transform and Bernstein functions’ technique.

Diffusion with stochastic resetting of interacting particles emerging in a model of population genetics

2021 ◽  
Author(s):  
Telles Timóteo Timóteo Da Silva ◽  
Marcelo Dutra Fragoso
Keyword(s):  
Population Genetics ◽  
Evolution Equations ◽  
Interacting Particles ◽  
Mathematical Technique ◽  
Individual Type ◽  
Multiple Interaction ◽  
Forward Equations ◽  
Fokker Planck Equations ◽  
Kolmogorov Forward Equations ◽  
And Diffusion

Abstract In this paper we put forward a Generalized Ohta-Kimura ladder model (GOKM) which bears a strong liaison with the so-called jump-type Fleming-Viot process (JFVP). The novelty here, when we compare with the classical Ohta-Kimura model, is that we now have an operator which allows multiple interaction among the individuals. It has to do with a generalized branching mechanism: m individual types extinguish and one individual type splits into m copies. The system of evolution equations arising from GOKM can be seen as a system of n-dimensional Kolmogorov forward equations (or Fokker-Planck equations). Besides the interest in its own right a favorable feature of GOKM, vis-`a-vis JFVP, is that its analysis requires a more amenable armory of concepts and mathematical technique to analyze some relevant issues such as correlation, indistinguishability of individuals and stationarity. In addition, as a by product, we show that the connection between Ohta-Kimura Model and diffusion with resetting, as previously structured in [6], can be extended to our setting.

Existence and regularity of mild solutions to fractional stochastic evolution equations

2018 ◽  
Vol 13 (1) ◽  
pp. 15 ◽  
Author(s):  
G.A. Zou ◽  
B. Wang ◽  
Y. Zhou
Keyword(s):  
Wave Equations ◽  
Multiplicative Noise ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Stochastic Evolution Equations ◽  
Diffusion Wave ◽  
Regularity Properties ◽  
Analysis Theory ◽  
And Diffusion ◽  
Selection Of

This study is concerned with the stochastic fractional diffusion and diffusion-wave equations driven by multiplicative noise. We prove the existence and uniqueness of mild solutions to these equations by means of the Picard’s iteration method. With the help of the fractional calculus and stochastic analysis theory, we also establish the pathwise spatial-temporal (Sobolev-Hölder) regularity properties of mild solutions to these types of fractional SPDEs in a semigroup framework. Finally, we relate our results to the selection of appropriate numerical schemes for the solutions of these time-fractional SPDEs.

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