The projection process along a simple closed smooth curve of a nonexplosive diffusion process on a cornplete Riemannian manifold is defined in probabilistic way. The winding numbers of the pmjection process are clockw...The projection process along a simple closed smooth curve of a nonexplosive diffusion process on a cornplete Riemannian manifold is defined in probabilistic way. The winding numbers of the pmjection process are clockwise and counterclockwise given. The symmetry of the diffusion process is shown to be equivalent to that for any closed smooth curve. the long time average winding numbers of the projection process in two different directions are equal.展开更多
To simulate a multivariate density with multi_hump, Markov chainMonte Carlo method encounters the obstacle of escaping from one hump to another, since it usually takes extraordinately long time and then becomes practi...To simulate a multivariate density with multi_hump, Markov chainMonte Carlo method encounters the obstacle of escaping from one hump to another, since it usually takes extraordinately long time and then becomes practically impossible to perform. To overcome these difficulties, a reversible scheme to generate a Markov chain, in terms of which the simulated density may be successful in rather general cases of practically avoiding being trapped in local humps, was suggested.展开更多
The closed form of the entropy production of stationary diffusion processes with bounded Nelson’s current velocity is given.The limit of the entropy productions of a sequence of reflecting diffusions is also discussed.
In this paper, the winding of stationary diffusions are studied. It is shown that, differently from Brownian motions,stationary diffusions wind up to time t angles in order of t, while Brownian motions wind up angles ...In this paper, the winding of stationary diffusions are studied. It is shown that, differently from Brownian motions,stationary diffusions wind up to time t angles in order of t, while Brownian motions wind up angles in order of logt,and the winding rates tend to , where c, an-i c2 are constants and is a Cauchy random variable.Moreover, it is proved that a stationary diffusion is reversible iff c2=0 for the winding around every point.展开更多
In this paper, we prove Ruelle’s inequality for the entropy and Lyapunov exponents of random diffeomorphisms. Y. Kefer has studied this problem in ergodic case, but his theorem and proof seem to be incorrect. A new d...In this paper, we prove Ruelle’s inequality for the entropy and Lyapunov exponents of random diffeomorphisms. Y. Kefer has studied this problem in ergodic case, but his theorem and proof seem to be incorrect. A new discussion is given in this paper with some new ideas and methods to be introduced, especially for f∈Diff^2(M), we introduce a new definition of C^2-norm |f|c^2 and the concept of relation number r(f) which play an important role both in this paper and in general studies.展开更多
文摘The projection process along a simple closed smooth curve of a nonexplosive diffusion process on a cornplete Riemannian manifold is defined in probabilistic way. The winding numbers of the pmjection process are clockwise and counterclockwise given. The symmetry of the diffusion process is shown to be equivalent to that for any closed smooth curve. the long time average winding numbers of the projection process in two different directions are equal.
文摘To simulate a multivariate density with multi_hump, Markov chainMonte Carlo method encounters the obstacle of escaping from one hump to another, since it usually takes extraordinately long time and then becomes practically impossible to perform. To overcome these difficulties, a reversible scheme to generate a Markov chain, in terms of which the simulated density may be successful in rather general cases of practically avoiding being trapped in local humps, was suggested.
基金Project supported by Doctoral Programm Foundation of Institution of Higher Education. the National Natural Science Foundation of China and 863 Programm.
文摘The closed form of the entropy production of stationary diffusion processes with bounded Nelson’s current velocity is given.The limit of the entropy productions of a sequence of reflecting diffusions is also discussed.
文摘In this paper, the winding of stationary diffusions are studied. It is shown that, differently from Brownian motions,stationary diffusions wind up to time t angles in order of t, while Brownian motions wind up angles in order of logt,and the winding rates tend to , where c, an-i c2 are constants and is a Cauchy random variable.Moreover, it is proved that a stationary diffusion is reversible iff c2=0 for the winding around every point.
文摘In this paper, we prove Ruelle’s inequality for the entropy and Lyapunov exponents of random diffeomorphisms. Y. Kefer has studied this problem in ergodic case, but his theorem and proof seem to be incorrect. A new discussion is given in this paper with some new ideas and methods to be introduced, especially for f∈Diff^2(M), we introduce a new definition of C^2-norm |f|c^2 and the concept of relation number r(f) which play an important role both in this paper and in general studies.
