In this paper we study the L^(p)-convergence rate of the tamed Euler scheme for scalar stochastic differential equations(SDEs)with piecewise continuous drift coefficient.More precisely,under the assumptions that the d...In this paper we study the L^(p)-convergence rate of the tamed Euler scheme for scalar stochastic differential equations(SDEs)with piecewise continuous drift coefficient.More precisely,under the assumptions that the drift coefficient is piecewise continuous and polynomially growing and that the diffusion coefficient is Lipschitz continuous and non-zero at the discontinuity points of the drift coefficient,we show that the SDE has a unique strong solution and the L^(p)-convergence order of the tamed Euler scheme is at least 1/2 for all p∈[1,∞).Moreover,a numerical example is provided to support our conclusion.展开更多
The Fokker–Planck–Kolmogorov（FPK） equation plays an essential role in nonlinear stochastic dynamics. However, neither analytical nor numerical solution is available as yet to FPK equations for high-dimensional sys...The Fokker–Planck–Kolmogorov（FPK） equation plays an essential role in nonlinear stochastic dynamics. However, neither analytical nor numerical solution is available as yet to FPK equations for high-dimensional systems. In the present paper, the dimension reduction of FPK equation for systems excited by additive white noise is studied. In the proposed method, probability density evolution method（PDEM）, in which a decoupled generalized density evolution equation is solved, is employed to reproduce the equivalent flux of probability for the marginalized FPK equation. A further step of constructing an equivalent coefficient finally completes the dimension-reduction of FPK equation. Examples are illustrated to verify the proposed method.展开更多
In calculating the seismic response of a building, the Spanish Instructions NCSE-02 and CTE, paragraph 3.7.7 （also EUROCODE 8 paragraph 1.2 part 1-1）, establish that if for all storeys the interstorey drift sensitiv...In calculating the seismic response of a building, the Spanish Instructions NCSE-02 and CTE, paragraph 3.7.7 （also EUROCODE 8 paragraph 1.2 part 1-1）, establish that if for all storeys the interstorey drift sensitivity coefficient, ζ, is less than or equal to 0.1, then it will not be necessary to consider the effects of the 2nd order （ P-△ effects）. In this paper the authors review this claim, because even for ≤0.1, increases of the bending moment at the ends of the columns due to the inclusion of second order effects can account for between 15% and 34% of its value for static service loads. This is significant since most adverse effects are shown in the lower height buildings （up to 5 floors） which it is precisely the range in which most of the housing stock of Spain is located. Finally, the authors delimit the coefficient for buildings of lesser height （up to 5 floors）, proposing to lower it generally to ζ≤ 006.展开更多
Stochastic fractional differential systems are important and useful in the mathematics,physics,and engineering fields.However,the determination of their probabilistic responses is difficult due to their non-Markovian ...Stochastic fractional differential systems are important and useful in the mathematics,physics,and engineering fields.However,the determination of their probabilistic responses is difficult due to their non-Markovian property.The recently developed globally-evolving-based generalized density evolution equation(GE-GDEE),which is a unified partial differential equation(PDE)governing the transient probability density function(PDF)of a generic path-continuous process,including non-Markovian ones,provides a feasible tool to solve this problem.In the paper,the GE-GDEE for multi-dimensional linear fractional differential systems subject to Gaussian white noise is established.In particular,it is proved that in the GE-GDEE corresponding to the state-quantities of interest,the intrinsic drift coefficient is a time-varying linear function,and can be analytically determined.In this sense,an alternative low-dimensional equivalent linear integer-order differential system with exact closed-form coefficients for the original highdimensional linear fractional differential system can be constructed such that their transient PDFs are identical.Specifically,for a multi-dimensional linear fractional differential system,if only one or two quantities are of interest,GE-GDEE is only in one or two dimensions,and the surrogate system would be a one-or two-dimensional linear integer-order system.Several examples are studied to assess the merit of the proposed method.Though presently the closed-form intrinsic drift coefficient is only available for linear stochastic fractional differential systems,the findings in the present paper provide a remarkable demonstration on the existence and eligibility of GE-GDEE for the case that the original high-dimensional system itself is non-Markovian,and provide insights for the physical-mechanism-informed determination of intrinsic drift and diffusion coefficients of GE-GDEE of more generic complex nonlinear systems.展开更多
Well-Posedness for McKean-Vlasov SDEs Driven by Multiplicative Stable Noises Changsong Deng Xi ng Huang Abstract We establish the well-posedness for a class of McKean-Vlasov SDEs driven by symmetric Q-stable Levy proc...Well-Posedness for McKean-Vlasov SDEs Driven by Multiplicative Stable Noises Changsong Deng Xi ng Huang Abstract We establish the well-posedness for a class of McKean-Vlasov SDEs driven by symmetric Q-stable Levy processes(1/2<α≤1),where the drift coefficient is Holder continuous in space variable,while the noise coeficient is Lipscitz continuous in space variable,and both of them satisfy the Lipschitz condition in distribution variable with respect to Wasserstein distance.If the drift coefficient does not depend on distribution variable,our methodology developed in this paper applies to the caseαe(0,1].The main tool relies on heat kernel estimates for(distribution independent)stable SDEs and Banach's fixed point theorem.展开更多
We study tile local linear estimator for tile drift coefficient of stochastic differential equations driven by α-stable Levy motions observed at discrete instants. Under regular conditions, we derive the weak consis-...We study tile local linear estimator for tile drift coefficient of stochastic differential equations driven by α-stable Levy motions observed at discrete instants. Under regular conditions, we derive the weak consis- tency and central limit theorem of the estimator. Compared with Nadaraya-Watson estimator, the local linear estimator has a bias reduction whether the kernel function is symmetric or not under different schemes. A silnu- lation study demonstrates that the local linear estimator performs better than Nadaraya-Watson estimator, especially on the boundary.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12371417,11971488)。
文摘In this paper we study the L^(p)-convergence rate of the tamed Euler scheme for scalar stochastic differential equations(SDEs)with piecewise continuous drift coefficient.More precisely,under the assumptions that the drift coefficient is piecewise continuous and polynomially growing and that the diffusion coefficient is Lipschitz continuous and non-zero at the discontinuity points of the drift coefficient,we show that the SDE has a unique strong solution and the L^(p)-convergence order of the tamed Euler scheme is at least 1/2 for all p∈[1,∞).Moreover,a numerical example is provided to support our conclusion.
基金supported by the National Natural Science Foundation of China(11172210)the Shuguang Program of Shanghai City(11SG21)
文摘The Fokker–Planck–Kolmogorov（FPK） equation plays an essential role in nonlinear stochastic dynamics. However, neither analytical nor numerical solution is available as yet to FPK equations for high-dimensional systems. In the present paper, the dimension reduction of FPK equation for systems excited by additive white noise is studied. In the proposed method, probability density evolution method（PDEM）, in which a decoupled generalized density evolution equation is solved, is employed to reproduce the equivalent flux of probability for the marginalized FPK equation. A further step of constructing an equivalent coefficient finally completes the dimension-reduction of FPK equation. Examples are illustrated to verify the proposed method.
文摘In calculating the seismic response of a building, the Spanish Instructions NCSE-02 and CTE, paragraph 3.7.7 （also EUROCODE 8 paragraph 1.2 part 1-1）, establish that if for all storeys the interstorey drift sensitivity coefficient, ζ, is less than or equal to 0.1, then it will not be necessary to consider the effects of the 2nd order （ P-△ effects）. In this paper the authors review this claim, because even for ≤0.1, increases of the bending moment at the ends of the columns due to the inclusion of second order effects can account for between 15% and 34% of its value for static service loads. This is significant since most adverse effects are shown in the lower height buildings （up to 5 floors） which it is precisely the range in which most of the housing stock of Spain is located. Finally, the authors delimit the coefficient for buildings of lesser height （up to 5 floors）, proposing to lower it generally to ζ≤ 006.
基金The supports of the National Natural Science Foundation of China(Grant Nos.51725804 and U1711264)the Research Fund for State Key Laboratories of Ministry of Science and Technology of China(SLDRCE19-B-23)the Shanghai Post-Doctoral Excellence Program(2022558)。
文摘Stochastic fractional differential systems are important and useful in the mathematics,physics,and engineering fields.However,the determination of their probabilistic responses is difficult due to their non-Markovian property.The recently developed globally-evolving-based generalized density evolution equation(GE-GDEE),which is a unified partial differential equation(PDE)governing the transient probability density function(PDF)of a generic path-continuous process,including non-Markovian ones,provides a feasible tool to solve this problem.In the paper,the GE-GDEE for multi-dimensional linear fractional differential systems subject to Gaussian white noise is established.In particular,it is proved that in the GE-GDEE corresponding to the state-quantities of interest,the intrinsic drift coefficient is a time-varying linear function,and can be analytically determined.In this sense,an alternative low-dimensional equivalent linear integer-order differential system with exact closed-form coefficients for the original highdimensional linear fractional differential system can be constructed such that their transient PDFs are identical.Specifically,for a multi-dimensional linear fractional differential system,if only one or two quantities are of interest,GE-GDEE is only in one or two dimensions,and the surrogate system would be a one-or two-dimensional linear integer-order system.Several examples are studied to assess the merit of the proposed method.Though presently the closed-form intrinsic drift coefficient is only available for linear stochastic fractional differential systems,the findings in the present paper provide a remarkable demonstration on the existence and eligibility of GE-GDEE for the case that the original high-dimensional system itself is non-Markovian,and provide insights for the physical-mechanism-informed determination of intrinsic drift and diffusion coefficients of GE-GDEE of more generic complex nonlinear systems.
文摘Well-Posedness for McKean-Vlasov SDEs Driven by Multiplicative Stable Noises Changsong Deng Xi ng Huang Abstract We establish the well-posedness for a class of McKean-Vlasov SDEs driven by symmetric Q-stable Levy processes(1/2<α≤1),where the drift coefficient is Holder continuous in space variable,while the noise coeficient is Lipscitz continuous in space variable,and both of them satisfy the Lipschitz condition in distribution variable with respect to Wasserstein distance.If the drift coefficient does not depend on distribution variable,our methodology developed in this paper applies to the caseαe(0,1].The main tool relies on heat kernel estimates for(distribution independent)stable SDEs and Banach's fixed point theorem.
基金supported by National Natural Science Foundation of China(Grant Nos.11171303 and 11071213)the Specialized Research Fund for the Doctor Program of Higher Education(Grant No.20090101110020)
文摘We study tile local linear estimator for tile drift coefficient of stochastic differential equations driven by α-stable Levy motions observed at discrete instants. Under regular conditions, we derive the weak consis- tency and central limit theorem of the estimator. Compared with Nadaraya-Watson estimator, the local linear estimator has a bias reduction whether the kernel function is symmetric or not under different schemes. A silnu- lation study demonstrates that the local linear estimator performs better than Nadaraya-Watson estimator, especially on the boundary.
