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.
|ジャーナル||Discrete and Continuous Dynamical Systems - Series S|
|出版ステータス||Published - 2021 3|
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics