研究者詳細 - 小守　良雄

論文 - 小守　良雄

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Split S-ROCK methods for high-dimensional stochastic differential equations 査読有り国際誌

Komori Y., Burrage K.

Journal of Scientific Computing 97 ( 3 ) Article number 62 2023年10月

担当区分：筆頭著者,　責任著者記述言語：英語掲載種別：研究論文（学術雑誌）

We propose explicit stochastic Runge–Kutta (RK) methods for high-dimensional Itô stochastic differential equations. By providing a linear error analysis and utilizing a Strang splitting-type approach, we construct them on the basis of orthogonal Runge–Kutta–Chebyshev methods of order 2. Our methods are of weak order 2 and have high computational accuracy for relatively large time-step size, as well as good stability properties. In addition, we take stochastic exponential RK methods of weak order 2 as competitors, and deal with implementation issues on Krylov subspace projection techniques for them. We carry out numerical experiments on a variety of linear and nonlinear problems to check the computational performance of the methods. As a result, it is shown that the proposed methods can be very effective on high-dimensional problems whose drift term has eigenvalues lying near the negative real axis and whose diffusion term does not have very large noise.

DOI： 10.1007/s10915-023-02354-8

Scopus

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85175646705&origin=inward

Formulae for mixed moments of Wiener processes and a stochastic area integral 査読有り国際誌

Komori Y., Yang G., Burrage K.

SIAM Journal on Numerical Analysis 61 ( 4 ) 1716 - 1736 2023年07月

担当区分：筆頭著者,　責任著者記述言語：英語掲載種別：研究論文（学術雑誌）

This paper deals with the expectation of monomials with respect to the stochastic area integral A1,2(t, t+h) =∫t+ht ∫st dW1(r)dW2(s)∫t+ht ∫st dW2(r)dW1(s) and the increments of two Wiener processes, Δ Wi(t, t+h) =Wi(t+h) Wi(t), i = 1, 2. In a monomial, if the exponent of one of the Wiener increments or the stochastic area integral is an odd number, then the expectation of the monomial is zero. However, if the exponent of any of them is an even number, then the expectation is nonzero and its exact value is not known in general. In the present paper, we derive formulae to give the value in general. As an application of the formulae, we will utilize the formulae for a careful stability analysis on a Magnus-type Milstein method. As another application, we will give some mixed moments of the increments of Wiener processes and stochastic double integrals.

DOI： 10.1137/22M152013X

Scopus

その他リンク： https://epubs.siam.org/doi/full/10.1137/22M152013X

A new class of structure-preserving stochastic exponential Runge-Kutta integrators for stochastic differential equations 査読有り国際誌

G. Yang, K. Burrage, Y. Komori, X. Ding

BIT Numerical Mathematics 62 ( 4 ) 1591 - 1623 2022年07月

記述言語：英語掲載種別：研究論文（学術雑誌）

In this article, a new class of stochastic exponential Runge-Kutta (SERK) methods is developed for solving stochastic differential equations. The proposed SERK methods can preserve conformal quadratic invariants and conformal symplectic structure automatically under certain coefficient conditions. Stochastic B-series theory is generalized, which allows the study of the mean-square convergence order conditions of the SERK methods. Some low stage stochastic exponential integrators with 1 order mean-square convergence and structure-preserving properties are given. For damped Hamiltonian systems with additive noise terms, a class of stochastic exponential integrators with 1.5 order mean-square convergence and conformal symplectic structure preservation is constructed. Numerical tests show the efficacy of the stochastic exponential integrators.

DOI： 10.1007/s10543-022-00924-0

Scopus

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85133393072&origin=inward

Integration of the stochastic underdamped harmonic oscillator by the theta-method 査読有り国際誌

Tocino A., Komori Y., Mitsui T.

Mathematics and Computers in Simulation 199 217 - 230 2022年03月

記述言語：英語掲載種別：研究論文（学術雑誌）

In recent papers, a simple harmonic oscillator with additive noise has been studied by several researchers, and it has been shown that its mean total energy increases linearly as time goes to infinity. In contrast to them, we consider an underdamped harmonic oscillator with additive noise. Our analysis reveals that the mean total energy of the stochastic underdamped harmonic oscillator remains bounded and it asymptotically tends to a certain value. In addition, we give a relation between the mean kinetic energy and the growth rate of the mean total energy. Whereas all stochastic -methods preserve this relation as they are of weak second local order, we show that only the stochastic trapezoidal method can attain the asymptotic values of the mean total energy and its derivative given by the exact solution. Numerical experiments are carried out to confirm these results.

DOI： 10.1016/j.matcom.2022.03.012

Scopus

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85128228142&origin=inward

A class of new Magnus-type methods for semi-linear non-commutative Itô stochastic differential equations 査読有り国際誌

Yang G., Burrage K., Komori Y., Burrage P., Ding X.

Numerical Algorithms 88 ( 4 ) 1641 - 1665 2021年01月

記述言語：英語掲載種別：研究論文（学術雑誌）

In this paper, a class of new Magnus-type methods is proposed for non-commutative Itô stochastic differential equations (SDEs) with semi-linear drift term and semi-linear diffusion terms, based on Magnus expansion for non-commutative linear SDEs. We construct a Magnus-type Euler method, a Magnus-type Milstein method and a Magnus-type Derivative-free method, and give the mean-square convergence analysis of these methods. Numerical tests are carried out to present the efficiency of the proposed methods compared with the corresponding underlying methods and the specific performance of the simulation Itô integral algorithms is investigated.

DOI： 10.1007/s11075-021-01089-7

Scopus

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85103401955&origin=inward

S-ROCK methods for stochastic delay differential equations with one fixed delay 査読有り国際誌

Komori Y., Eremin A., Burrage K.

Journal of Computational and Applied Mathematics 353 345 - 354 2019年06月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（学術雑誌）

© 2019 Elsevier B.V. We propose stabilized explicit stochastic Runge–Kutta methods of strong order one half for Itô stochastic delay differential equations with one fixed delay. The family of the methods is constructed by embedding Runge–Kutta–Chebyshev methods of order one for ordinary differential equations. The values of a damping parameter of the methods are determined appropriately in order to obtain excellent mean square stability properties. Numerical experiments are carried out to confirm their order of convergence and stability properties.

DOI： 10.1016/j.cam.2018.12.042

Kyutacar

Scopus

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85060101996&origin=inward

Weak second order explicit exponential RUNGE–KUTTA methods for stochastic differential equations 査読有り国際誌

Komori Y., Cohen D., Burrage K.

SIAM Journal on Scientific Computing 39 ( 6 ) A2857 - A2878 2017年01月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（学術雑誌）

© 2017 Society for Industrial and Applied Mathematics. We propose new explicit exponential Runge–Kutta methods for the weak approximation of solutions of stiff Itô stochastic differential equations (SDEs). We also consider the use of exponential Runge–Kutta methods in combination with splitting methods. These methods have weak order 2 for multidimensional, noncommutative SDEs with a semilinear drift term, whereas they are of order 2 or 3 for semilinear ordinary differential equations. These methods are A-stable in the mean square sense for a scalar linear test equation whose drift and diffusion terms have complex coefficients. We carry out numerical experiments to compare the performance of these methods with an existing explicit stabilized method of weak order 2.

DOI： 10.1137/15M1041341

Kyutacar

Scopus

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85040000641&origin=inward

Suitable algorithm associated with a parameterization for the three-parameter log-normal distribution 査読有り国際誌

Komori Y.

Communications in Statistics: Simulation and Computation 44 ( 1 ) 239 - 246 2015年01月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（学術雑誌）

Associated with a parameterization for the three-parameter lognormal distribution, an algorithm was proposed by Komori and Hirose, which can find a local maximum likelihood (ML) estimate surely if it exists. Nevertheless, by Vera and Daz-Garca it was shown that performance in finding a local ML estimate deteriorated by adopting the parameterization only and using other algorithm. In the present article, it will be shown that Komori and Hirose's algorithm should be used for the parameterization. This work will also give MATLAB codes as a useful tool for the parameter estimation of the distribution. Copyright © Taylor & Francis Group, LLC.

DOI： 10.1080/03610918.2013.773343

Kyutacar

Scopus

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84905484569&origin=inward

A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems 査読有り国際誌

Komori Y., Burrage K.

BIT Numerical Mathematics 54 ( 4 ) 1067 - 1085 2014年01月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（学術雑誌）

© 2014, Springer Science+Business Media Dordrecht.In order to simulate stiff biochemical reaction systems, an explicit exponential Euler scheme is derived for multi-dimensional, non-commutative stochastic differential equations with a semilinear drift term. The scheme is of strong order one half and A-stable in mean square. The combination with this and the projection method shows good performance in numerical experiments dealing with an alternative formulation of the chemical Langevin equation for a human ether a-go-go related gene ion channel model.

DOI： 10.1007/s10543-014-0485-1

Kyutacar

Scopus

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Stochastic Runge-Kutta methods with deterministic high order for ordinary differential equations 査読有り国際誌

Komori Y., Buckwar E.

BIT Numerical Mathematics 53 ( 3 ) 617 - 639 2013年09月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（学術雑誌）

We consider embedding deterministic Runge-Kutta methods with high order into weak order stochastic Runge-Kutta (SRK) methods for non-commutative stochastic differential equations (SDEs). As a result, we have obtained weak second order SRK methods which have good properties with respect to not only practical errors but also mean square stability. In our stability analysis, as well as a scalar test equation with complex-valued parameters, we have used a multi-dimensional non-commutative test SDE. The performance of our new schemes will be shown through comparisons with an efficient and optimal weak second order scheme proposed by Debrabant and Rößler (Appl. Numer. Math. 59:582-594, 2009). © 2013 Springer Science+Business Media Dordrecht.

DOI： 10.1007/s10543-013-0419-3

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Strong first order S-ROCK methods for stochastic differential equations 査読有り国際誌

Komori Y., Burrage K.

Journal of Computational and Applied Mathematics 242 ( 1 ) 261 - 274 2013年04月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（学術雑誌）

Explicit stochastic Runge-Kutta (SRK) methods are constructed for non-commutative Itô and Stratonovich stochastic differential equations. Our aim is to derive explicit SRK schemes of strong order one, which are derivative free and have large stability regions. In the present paper, this will be achieved by embedding Chebyshev methods for ordinary differential equations in SRK methods proposed by Rößler (2010). In order to check their convergence order, stability properties and computational efficiency, some numerical experiments will be performed. © 2012 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.cam.2012.10.026

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その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84870302486&origin=inward

Weak second order S-ROCK methods for Stratonovich stochastic differential equations 査読有り国際誌

Komori Y., Burrage K.

Journal of Computational and Applied Mathematics 236 ( 11 ) 2895 - 2908 2012年05月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（学術雑誌）

It is well known that the numerical solution of stiff stochastic ordinary differential equations leads to a step size reduction when explicit methods are used. This has led to a plethora of implicit or semi-implicit methods with a wide variety of stability properties. However, for stiff stochastic problems in which the eigenvalues of a drift term lie near the negative real axis, such as those arising from stochastic partial differential equations, explicit methods with extended stability regions can be very effective. In the present paper our aim is to derive explicit RungeKutta schemes for non-commutative Stratonovich stochastic differential equations, which are of weak order two and which have large stability regions. This will be achieved by the use of a technique in Chebyshev methods for ordinary differential equations. © 2012 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.cam.2012.01.033

Kyutacar

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その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84857789300&origin=inward

Supplement: Efficient weak second order stochastic RungeKutta methods for non-commutative Stratonovich stochastic differential equations 査読有り国際誌

Komori Y., Burrage K.

Journal of Computational and Applied Mathematics 235 ( 17 ) 5326 - 5329 2011年07月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（学術雑誌）

This paper gives a modification of a class of stochastic RungeKutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly. © 2011 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.cam.2011.04.021

Kyutacar

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Statistical analysis related to impulse tests for self-restoring insulation 査読有り国際誌

小守　良雄

IEEJ Transactions on Electrical and Elecronic Engineering 3 ( 6 ) 680 - 687 2008年11月

Weak first- or second-order implicit Runge-Kutta methods forstochastic differential equations with a scalar Wiener process 査読有り国際誌

Y. Komori

Journal of Computational and Applied Mathematics 217 ( 1 ) 166 - 179 2008年07月

Weak second order stochastic Runge-Kutta methods for non-commutative stochastic differential equations 査読有り

Y. Komori

Journal of Computational and Applied Mathematics 206 ( 1 ) 158 - 173 2007年09月

Weak order stochastic Runge-Kutta methods for commutative stochastic differential equations 査読有り

Y. Komori

Journal of Computational and Applied Mathematics 203 ( 1 ) 57 - 79 2007年06月

Multi-colored rooted tree analysis of the weak order conditions of a stochastic Runge-Kutta family 査読有り

Y. Komori

Applied Numerical Mathematics 57 ( 2 ) 147 - 165 2007年02月

Properties of the Weibull cumulative exposure model 査読有り

Y. Komori

Journal of Applied Statistics 33 ( 1 ) 17 - 34 2006年01月

Easy estimation by a new parameterization for the three-parameter lognormal distribution 査読有り

Y. Komori,H. Hirose

Journal of Statistical Computation and Simulation 74 ( 1 ) 63 - 74 2004年01月

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