Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Types of Limits II

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...

Probability Distributions

Probability Distributions

The probability of a random variable x is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...

Types of Limits I

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...

Radical Chain-Growth Polymerization: Chain Branching

Radical Chain-Growth Polymerization: Chain Branching

The skeletal structure of polymers synthesized via radical polymerization is always branched. For example, the polymerization of ethylene by radical polymerization results in a low-density grade of polyethylene with a heavily branched skeletal structure. Here, the radical site abstracts hydrogen from the growing chain, and the radical site shifts from the end (a primary carbon center) to anywhere within the growing chain (a secondary carbon center). Consequently, the part of the chain from the...

Distributions to Estimate Population Parameter

Distributions to Estimate Population Parameter

The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...

Parametric Survival Analysis: Weibull and Exponential Methods

Parametric Survival Analysis: Weibull and Exponential Methods

Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...

You might also read

Related Articles

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

Sort by

Same author

MULTITYPE BRANCHING PROCESSES WITH INHOMOGENEOUS POISSON IMMIGRATION.

Advances in applied probability·2025

Same author

A branching stochastic evolutionary model of the B-cell repertoire.

Journal of mathematical biology·2024

Same author

Statistical modelling of COVID-19 pandemic development applying branching processes.

Journal of applied statistics·2023

Same author

Subcritical Sevastyanov branching processes with nonhomogeneous Poisson immigration.

Journal of applied probability·2019

Same author

A test of homogeneity for age-dependent branching processes with immigration.

Electronic journal of statistics·2016

Same author

Two-Type Age-Dependent Branching Processes with Inhomogeneous Immigration as Models of Renewing Cell Populations.

Pliska. Pliiska·2013

Search research articles

Related Experiment Video

Updated: May 7, 2026

Simultaneous Assessment of Kinship, Division Number, and Phenotype via Flow Cytometry for Hematopoietic Stem and Progenitor Cells

Simultaneous Assessment of Kinship, Division Number, and Phenotype via Flow Cytometry for Hematopoietic Stem and Progenitor Cells

Published on: March 24, 2023

Limiting Distributions for Multitype Branching Processes.

Andrei Y Yakovlev¹, Nikolay M Yanev

¹University of Rochester and Institute of Mathematics, Sofia.

Stochastic Analysis and Applications

|September 14, 2013

Summary

This study analyzes multitype Markov branching processes, proving multivariate asymptotic normality for both process behavior and relative frequencies. These findings are crucial for cell kinetics research.

Keywords:

limit theorems multitype branching processes multivariate asymptotic normality relative frequencies

More Related Videos

A Concoction Pipeline for Generating Molecular Operational Taxonomic Units (MOTUs) Among Riparian and Aquatic Beetles

A Concoction Pipeline for Generating Molecular Operational Taxonomic Units (MOTUs) Among Riparian and Aquatic Beetles

Published on: July 11, 2025

Quantifying Branching Density in Rat Mammary Gland Whole-mounts Using the Sholl Analysis Method

Quantifying Branching Density in Rat Mammary Gland Whole-mounts Using the Sholl Analysis Method

Published on: July 12, 2017

Related Experiment Videos

Last Updated: May 7, 2026

Simultaneous Assessment of Kinship, Division Number, and Phenotype via Flow Cytometry for Hematopoietic Stem and Progenitor Cells

Simultaneous Assessment of Kinship, Division Number, and Phenotype via Flow Cytometry for Hematopoietic Stem and Progenitor Cells

Published on: March 24, 2023

A Concoction Pipeline for Generating Molecular Operational Taxonomic Units (MOTUs) Among Riparian and Aquatic Beetles

A Concoction Pipeline for Generating Molecular Operational Taxonomic Units (MOTUs) Among Riparian and Aquatic Beetles

Published on: July 11, 2025

Quantifying Branching Density in Rat Mammary Gland Whole-mounts Using the Sholl Analysis Method

Quantifying Branching Density in Rat Mammary Gland Whole-mounts Using the Sholl Analysis Method

Published on: July 12, 2017

Area of Science:

Probability Theory
Stochastic Processes
Mathematical Biology

Background:

Markov branching processes are fundamental models in probability.
Understanding asymptotic behavior is key for long-term predictions.
Previous work focused on fixed time, limiting the scope for dynamic systems.

Purpose of the Study:

Investigate the asymptotic behavior of multitype Markov branching processes.
Obtain limiting distributions and prove multivariate asymptotic normality.
Analyze relative frequencies of distinct types for biological applications.

Main Methods:

Asymptotic analysis of Markov branching processes.
Techniques for discrete and continuous time models.
Mathematical derivations for limiting distributions and normality.

Main Results:

Established asymptotic behavior for large initial ancestors and infinite time.
Proved multivariate asymptotic normality for the processes.
Derived non-random limits for relative frequencies, showing asymptotic normality.

Conclusions:

The study provides new limiting results for Markov branching processes.
Findings are particularly relevant for cell kinetics where relative frequencies are measurable.
Extends previous research by considering infinite time horizons.