Using Girsanov transformation,we derive a new link from stochastic differential equations of Markovian type to nonlinear parabolic equations of Burgers-KPZ type,in such a manner that the obtained BurgersKPZ equation c...Using Girsanov transformation,we derive a new link from stochastic differential equations of Markovian type to nonlinear parabolic equations of Burgers-KPZ type,in such a manner that the obtained BurgersKPZ equation characterizes the path-independence property of the density process of Girsanov transformation for the stochastic differential equation.Our assertion also holds for SDEs on a connected differential manifold.展开更多
Based on a recent result on linking stochastic differential equations on R^d to （finite-dimensional） Burger-KPZ type nonlinear parabolic partial differential equations, we utilize Galerkin type finite-dimensional ap...Based on a recent result on linking stochastic differential equations on R^d to （finite-dimensional） Burger-KPZ type nonlinear parabolic partial differential equations, we utilize Galerkin type finite-dimensional approximations to characterize the path-independence of the density process of Girsanov transformation for the infinite-dimensionl stochastic evolution equations. Our result provides a link of infinite-dimensional semi-linear stochastic differential equations to infinite-dimensional Burgers-KPZ type nonlinear parabolic partial differential equations. As an application, this characterization result is applied to stochastic heat equation in one space dimension over the unit interval.展开更多
We study the free energy fluctuations for a mixture of directed polymers,which was first introduced by Borodin et al.(2015)to investigate the limiting distribution of a stationary Kardar-Parisi-Zhang(KPZ)equation.The ...We study the free energy fluctuations for a mixture of directed polymers,which was first introduced by Borodin et al.(2015)to investigate the limiting distribution of a stationary Kardar-Parisi-Zhang(KPZ)equation.The main results consist of both the law of large numbers and the asymptotic fluctuation for the free energy as the model size tends to infinity.In particular,we find the explicit values(which may depend on model parameters)of normalizing constants in the fluctuation.This shows that such a mixture model is in the KPZ university class.展开更多
基金supported by Laboratory of Mathematics and Complex Systems,National Natural Science Foundation of China(Grant No.11131003)Specialized Research Fund for the Doctoral Program of Higher Educationthe Fundamental Research Funds for the Central Universities
文摘Using Girsanov transformation,we derive a new link from stochastic differential equations of Markovian type to nonlinear parabolic equations of Burgers-KPZ type,in such a manner that the obtained BurgersKPZ equation characterizes the path-independence property of the density process of Girsanov transformation for the stochastic differential equation.Our assertion also holds for SDEs on a connected differential manifold.
文摘Based on a recent result on linking stochastic differential equations on R^d to （finite-dimensional） Burger-KPZ type nonlinear parabolic partial differential equations, we utilize Galerkin type finite-dimensional approximations to characterize the path-independence of the density process of Girsanov transformation for the infinite-dimensionl stochastic evolution equations. Our result provides a link of infinite-dimensional semi-linear stochastic differential equations to infinite-dimensional Burgers-KPZ type nonlinear parabolic partial differential equations. As an application, this characterization result is applied to stochastic heat equation in one space dimension over the unit interval.
基金supported by National Natural Science Foundation of China (Grant No. 11371317)the Fundamental Research Funds for the Central Universities
文摘We study the free energy fluctuations for a mixture of directed polymers,which was first introduced by Borodin et al.(2015)to investigate the limiting distribution of a stationary Kardar-Parisi-Zhang(KPZ)equation.The main results consist of both the law of large numbers and the asymptotic fluctuation for the free energy as the model size tends to infinity.In particular,we find the explicit values(which may depend on model parameters)of normalizing constants in the fluctuation.This shows that such a mixture model is in the KPZ university class.
