Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Types of Limits II01:24

Types of Limits II

When observing how a curve behaves near a specific point along the horizontal axis, there are cases where the curve’s height increases or decreases without limit as the position draws closer to that point. The curve does not settle at any particular value; instead, the values grow more extreme—upward or downward—the nearer they get. No defined value exists exactly at that location, yet the surrounding behavior becomes more dramatic, indicating a sharp change in direction.The values may rise...
The Squeeze Theorem01:30

The Squeeze Theorem

Certain mathematical functions exhibit unpredictable or highly variable behavior near specific input values, making direct evaluation of their limits challenging. This complexity may arise from rapid oscillations or irregular patterns that obscure the function’s trend. In such cases, the Squeeze Theorem offers a reliable method for determining limits.According to the Squeeze Theorem, if a function is confined between two other functions near a particular point, and both outer functions approach...
Limit Laws II01:26

Limit Laws II

In calculus, limit laws serve as foundational tools for evaluating the behavior of functions as inputs approach specific values. Among these, the laws concerning quotients, powers, and roots are particularly useful in breaking down complex expressions.The Quotient Law allows the limit of a division between two functions to be calculated by dividing their individual limits, provided the limit of the denominator exists and is not zero. For example,The Power Law states that the limit of a function...
Types of Limits I01:23

Types of Limits I

Limits are a key mathematical concept for understanding how functions behave as their input approaches specific values, particularly when the function is undefined. They help reveal trends and discontinuities by examining the values a function approaches rather than its actual value.One-sided limits focus on the direction from which a value is approached. When a function behaves differently depending on whether the input approaches from the left or the right, the two one-sided limits may not...
Limits with Oscillating Discontinuities01:19

Limits with Oscillating Discontinuities

An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the most...
Limits of Multivariable Functions01:25

Limits of Multivariable Functions

Limits of multivariable functions describe how a function behaves as its input approaches a particular point in the plane. In single-variable calculus, a limit examines the behavior of a function as the input approaches a number from two directions along a line. For functions of two variables, the situation is more complex because the input can approach a point from infinitely many paths in the xy-plane. A limit exists only when the function approaches the same value along every possible...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

What Are University Professors' Motivations? A Realistic Approach to Self-Perception of a Group of Spanish University Professors Belonging to the G-9 Group of Universities.

International journal of environmental research and public health·2021
See all related articles

Related Experiment Video

Updated: Jun 20, 2026

Experimental Manipulation of Body Size to Estimate Morphological Scaling Relationships in Drosophila
06:00

Experimental Manipulation of Body Size to Estimate Morphological Scaling Relationships in Drosophila

Published on: October 1, 2011

A scaling limit theorem for controlled branching processes with a size-divisible term.

Miguel González1,2, Pedro Martín-Chávez3,1, Inés Del Puerto1,2

  • 1Departamento de Matemáticas, Universidad de Extremadura, 06006 Badajoz, Spain.

Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales. Serie A, Matematicas
|June 19, 2026
PubMed
Summary

This study provides conditions for controlled branching processes to converge weakly. The research introduces a new control mechanism for population dynamics, leading to a continuous-state branching process with dependent immigration.

Keywords:
Branching processInfinitesimal generatorLimit theoremMartingale problemScaling limitWeak convergence

More Related Videos

Surgical Size Reduction of Zebrafish for the Study of Embryonic Pattern Scaling
06:31

Surgical Size Reduction of Zebrafish for the Study of Embryonic Pattern Scaling

Published on: May 3, 2019

Related Experiment Videos

Last Updated: Jun 20, 2026

Experimental Manipulation of Body Size to Estimate Morphological Scaling Relationships in Drosophila
06:00

Experimental Manipulation of Body Size to Estimate Morphological Scaling Relationships in Drosophila

Published on: October 1, 2011

Surgical Size Reduction of Zebrafish for the Study of Embryonic Pattern Scaling
06:31

Surgical Size Reduction of Zebrafish for the Study of Embryonic Pattern Scaling

Published on: May 3, 2019

Area of Science:

  • Stochastic processes
  • Probability theory
  • Mathematical biology

Background:

  • Branching processes are fundamental models in population dynamics.
  • Existing models often have limitations in capturing complex population control mechanisms.

Purpose of the Study:

  • To establish sufficient conditions for the weak convergence of controlled branching processes.
  • To extend existing control mechanisms by decomposing random variables into immigration and size-divisible components.

Main Methods:

  • Utilizing probability generating functions for offspring and control laws.
  • Applying tightness arguments and martingale problem identification.
  • Decomposing control variables into independent immigration and size-divisible terms.

Main Results:

  • Demonstrated weak convergence of controlled branching processes on the Skorokhod space.
  • Characterized a broad range of control functions, including Poisson, binomial, and negative binomial distributions.
  • Identified the limit process as a continuous-state branching process with dependent immigration.

Conclusions:

  • The proposed control mechanism offers a flexible extension for branching process models.
  • The findings contribute to a deeper understanding of population dynamics under various control strategies.
  • The limit process can simplify to a Feller branching diffusion with immigration in specific cases.