Numerical and mathematical analysis of blow-up problems for a stochastic differential equation

Tetsuya Ishiwata; Young Chol Yang

doi:10.3934/dcdss.2020391

Numerical and mathematical analysis of blow-up problems for a stochastic differential equation

Tetsuya Ishiwata, Young Chol Yang

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We consider the blow-up problems of the power type of stochastic differential equation, dX = αX^p(t)dt + X^q(t)dW(t). It has been known that there exists a critical exponent such that if p is greater than the critical exponent then the solution X(t) blows up almost surely in the finite time. In our research, focus on this critical exponent, we propose a numerical scheme by adaptive time step and analyze it mathematically. Finally we show the numerical result by using the proposed scheme.

Original language	English
Pages (from-to)	909-918
Number of pages	10
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	14
Issue number	3
DOIs	https://doi.org/10.3934/dcdss.2020391
Publication status	Published - 2021 Mar

Keywords

Adaptive time step control
Blow-up
Blow-up time
Euler-Maruyama scheme
SDE

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.3934/dcdss.2020391

Cite this

@article{d45093018aee4135962f82033b3622d2,

title = "Numerical and mathematical analysis of blow-up problems for a stochastic differential equation",

abstract = "We consider the blow-up problems of the power type of stochastic differential equation, dX = αXp(t)dt + Xq(t)dW(t). It has been known that there exists a critical exponent such that if p is greater than the critical exponent then the solution X(t) blows up almost surely in the finite time. In our research, focus on this critical exponent, we propose a numerical scheme by adaptive time step and analyze it mathematically. Finally we show the numerical result by using the proposed scheme.",

keywords = "Adaptive time step control, Blow-up, Blow-up time, Euler-Maruyama scheme, SDE",

author = "Tetsuya Ishiwata and Yang, {Young Chol}",

year = "2021",

month = mar,

doi = "10.3934/dcdss.2020391",

language = "English",

volume = "14",

pages = "909--918",

journal = "Discrete and Continuous Dynamical Systems - Series S",

issn = "1937-1632",

publisher = "American Institute of Mathematical Sciences",

number = "3",

}

TY - JOUR

T1 - Numerical and mathematical analysis of blow-up problems for a stochastic differential equation

AU - Ishiwata, Tetsuya

AU - Yang, Young Chol

PY - 2021/3

Y1 - 2021/3

N2 - We consider the blow-up problems of the power type of stochastic differential equation, dX = αXp(t)dt + Xq(t)dW(t). It has been known that there exists a critical exponent such that if p is greater than the critical exponent then the solution X(t) blows up almost surely in the finite time. In our research, focus on this critical exponent, we propose a numerical scheme by adaptive time step and analyze it mathematically. Finally we show the numerical result by using the proposed scheme.

AB - We consider the blow-up problems of the power type of stochastic differential equation, dX = αXp(t)dt + Xq(t)dW(t). It has been known that there exists a critical exponent such that if p is greater than the critical exponent then the solution X(t) blows up almost surely in the finite time. In our research, focus on this critical exponent, we propose a numerical scheme by adaptive time step and analyze it mathematically. Finally we show the numerical result by using the proposed scheme.

KW - Adaptive time step control

KW - Blow-up

KW - Blow-up time

KW - Euler-Maruyama scheme

KW - SDE

UR - http://www.scopus.com/inward/record.url?scp=85099707807&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85099707807&partnerID=8YFLogxK

U2 - 10.3934/dcdss.2020391

DO - 10.3934/dcdss.2020391

M3 - Article

AN - SCOPUS:85099707807

SN - 1937-1632

VL - 14

SP - 909

EP - 918

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

IS - 3

ER -

Numerical and mathematical analysis of blow-up problems for a stochastic differential equation

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this