In this paper, the existence and smoothness of the collision local time are proved for two independent fractional Brownian motions, through L^2 convergence and Chaos expansion. Furthermore, the regularity of the colli...In this paper, the existence and smoothness of the collision local time are proved for two independent fractional Brownian motions, through L^2 convergence and Chaos expansion. Furthermore, the regularity of the collision local time process is studied.展开更多
Let { W(t);t≥0 } be a standard Brownian motion.For a positive integer m ,define a Gaussian processX m(t)=1m!∫ t 0(t-s) m d W(s).In this paper the liminf behavior of the increments of this process is discu...Let { W(t);t≥0 } be a standard Brownian motion.For a positive integer m ,define a Gaussian processX m(t)=1m!∫ t 0(t-s) m d W(s).In this paper the liminf behavior of the increments of this process is discussed by establishing some probability inequalities.Some previous results are extended and improved.展开更多
We introduce a super-Lévy process and study maximal speed of all particles in the range and the support of the super-Lévy process. The state of historical super-Lévy process is a measure on the set of p...We introduce a super-Lévy process and study maximal speed of all particles in the range and the support of the super-Lévy process. The state of historical super-Lévy process is a measure on the set of paths. We study the maximal speed of all particles during a given time period, which turns out to be a function of the packing dimension of the time period. We calculate the Hausdorff dimension of the set of a-fast paths in the support and the range of the historical super-Lévy process.展开更多
The moments and absolute continuity of measure valued branching Brownian motions with bounded interacting intensity are investigated. An estimate of higher order moments is obtained.The absolute continuity is verifie...The moments and absolute continuity of measure valued branching Brownian motions with bounded interacting intensity are investigated. An estimate of higher order moments is obtained.The absolute continuity is verified in the one dimension case. This thereby verifies the conjecture of Méléard and Roelly in .展开更多
Exponential trichotomy theory is developed and the Fredholm Alternative Lemma is proved for the system with exponential trichotomies. An application of thesetheories is also given to obtain the persistence condition f...Exponential trichotomy theory is developed and the Fredholm Alternative Lemma is proved for the system with exponential trichotomies. An application of thesetheories is also given to obtain the persistence condition for heteroclinic orbits connecting nonhyperbolic equilibria, which extends the corresponding result of .展开更多
基金the National Natural Science Foundation of China(No. 10471003).
文摘In this paper, the existence and smoothness of the collision local time are proved for two independent fractional Brownian motions, through L^2 convergence and Chaos expansion. Furthermore, the regularity of the collision local time process is studied.
基金Project Supported by National Science Fundation of China(1 9571 0 2 1 ) and Zhejiang Province
文摘Let { W(t);t≥0 } be a standard Brownian motion.For a positive integer m ,define a Gaussian processX m(t)=1m!∫ t 0(t-s) m d W(s).In this paper the liminf behavior of the increments of this process is discussed by establishing some probability inequalities.Some previous results are extended and improved.
基金Project supported by the National Natural Science Foundation of China(No.10571159)the Ph.D.Programs Foundation of Ministry of Education of China(No.20060335032)and the Foundation of Hangzhou Dianzi University(No.KYS091506042)
文摘We introduce a super-Lévy process and study maximal speed of all particles in the range and the support of the super-Lévy process. The state of historical super-Lévy process is a measure on the set of paths. We study the maximal speed of all particles during a given time period, which turns out to be a function of the packing dimension of the time period. We calculate the Hausdorff dimension of the set of a-fast paths in the support and the range of the historical super-Lévy process.
文摘The moments and absolute continuity of measure valued branching Brownian motions with bounded interacting intensity are investigated. An estimate of higher order moments is obtained.The absolute continuity is verified in the one dimension case. This thereby verifies the conjecture of Méléard and Roelly in .
文摘Exponential trichotomy theory is developed and the Fredholm Alternative Lemma is proved for the system with exponential trichotomies. An application of thesetheories is also given to obtain the persistence condition for heteroclinic orbits connecting nonhyperbolic equilibria, which extends the corresponding result of .
