# Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

## Abstract

This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.

- Authors:

- Dept. Mathematical Education, State Islamic University of Sultan Syarif Kasim Riau, 28293 Indonesia and Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor (Malaysia)
- Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor Malaysia and UTM Center for Industrial and Applied Mathematics (UTM-CIAM) (Malaysia)

- Publication Date:

- OSTI Identifier:
- 22391272

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 1651; Journal Issue: 1; Conference: SYMOMATH 2014: Symposium on Biomathematics, East Java (Indonesia), 31 Aug - 2 Sep 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; CHAPMAN-KOLMOGOROV EQUATION; DIFFUSION; EXACT SOLUTIONS; FOKKER-PLANCK EQUATION; MARKOV PROCESS; MATHEMATICAL MODELS

### Citation Formats

```
Granita, E-mail: granitafc@gmail.com, and Bahar, A.
```*Stochastic differential equation model for linear growth birth and death processes with immigration and emigration*. United States: N. p., 2015.
Web. doi:10.1063/1.4914435.

```
Granita, E-mail: granitafc@gmail.com, & Bahar, A.
```*Stochastic differential equation model for linear growth birth and death processes with immigration and emigration*. United States. doi:10.1063/1.4914435.

```
Granita, E-mail: granitafc@gmail.com, and Bahar, A. Mon .
"Stochastic differential equation model for linear growth birth and death processes with immigration and emigration". United States.
doi:10.1063/1.4914435.
```

```
@article{osti_22391272,
```

title = {Stochastic differential equation model for linear growth birth and death processes with immigration and emigration},

author = {Granita, E-mail: granitafc@gmail.com and Bahar, A.},

abstractNote = {This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.},

doi = {10.1063/1.4914435},

journal = {AIP Conference Proceedings},

number = 1,

volume = 1651,

place = {United States},

year = {Mon Mar 09 00:00:00 EDT 2015},

month = {Mon Mar 09 00:00:00 EDT 2015}

}

DOI: 10.1063/1.4914435

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