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

研究成果: Article › 査読

1 被引用数 (Scopus)

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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.

本文言語	English
ページ（範囲）	909-918
ページ数	10
ジャーナル	Discrete and Continuous Dynamical Systems - Series S
巻	14
号	3
DOI	https://doi.org/10.3934/dcdss.2020391
出版ステータス	Published - 2021 3月

ASJC Scopus subject areas

分析
離散数学と組合せ数学
応用数学

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

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

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AU - Ishiwata, Tetsuya

AU - Yang, Young Chol

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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

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JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

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

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