We use reflecting Brownian motion(RBM)to prove the well-known Gauss–Bonnet–Chern theorem for a compact Riemannian manifold with boundary.The boundary integrand is obtained by carefully analyzing the asymptotic behav...We use reflecting Brownian motion(RBM)to prove the well-known Gauss–Bonnet–Chern theorem for a compact Riemannian manifold with boundary.The boundary integrand is obtained by carefully analyzing the asymptotic behavior of the boundary local time of RBM for small times.展开更多
In this paper, we investigate Markovian backward stochastic differential equations(BSDEs) with the generator and the terminal value that depend on the solutions of stochastic differential equations with rankbased drif...In this paper, we investigate Markovian backward stochastic differential equations(BSDEs) with the generator and the terminal value that depend on the solutions of stochastic differential equations with rankbased drift coefficients. We study regularity properties of the solutions of this kind of BSDEs and establish their connection with semi-linear backward parabolic partial differential equations in simplex with Neumann boundary condition. As an application, we study the European option pricing problem with capital size based stock prices.展开更多
In Internet environment, traffic flow to a link is typically modeled by superposition of ON/OFF based sources. During each ON-period for a particular source, packets arrive according to a Poisson process and packet si...In Internet environment, traffic flow to a link is typically modeled by superposition of ON/OFF based sources. During each ON-period for a particular source, packets arrive according to a Poisson process and packet sizes (hence service times) can be generally distributed. In this paper, we establish heavy traffic limit theorems to provide suitable approximations for the system under first-in first-out (FIFO) and work-conserving service discipline, which state that, when the lengths of both ON- and OFF-periods are lightly tailed, the sequences of the scaled queue length and workload processes converge weakly to short-range dependent reflecting Gaussian processes, and when the lengths of ON- and/or OFF-periods are heavily tailed with infinite variance, the sequences converge weakly to either reflecting fractional Brownian motions (FBMs) or certain type of long- range dependent reflecting Gaussian processes depending on the choice of scaling as the number of superposed sources tends to infinity. Moreover, the sequences exhibit a state space collapse-like property when the number of sources is large enough, which is a kind of extension of the well-known Little's law for M/M/1 queueing system. Theory to justify the approximations is based on appropriate heavy traffic conditions which essentially mean that the service rate closely approaches the arrival rate when the number of input sources tends to infinity.展开更多
This paper studies a multitype re-entrant line under smaller-buffer-first-served policy, which is an extension of first-buffer-first-served re-entrant line. We prove a heavy traffic limit theorem. The key to the proof...This paper studies a multitype re-entrant line under smaller-buffer-first-served policy, which is an extension of first-buffer-first-served re-entrant line. We prove a heavy traffic limit theorem. The key to the proof is to prove the uniform convergence of the corresponding critical fluid model.展开更多
In this paper, we define a class of domains in R^n. Using the synchronous coupling of reflecting Brownian motion, we obtain the monotonicity property of the solution of the heat equation with the Neumann boundary cond...In this paper, we define a class of domains in R^n. Using the synchronous coupling of reflecting Brownian motion, we obtain the monotonicity property of the solution of the heat equation with the Neumann boundary conditions. We then show that the hot spots conjecture holds for this class of domains.展开更多
文摘We use reflecting Brownian motion(RBM)to prove the well-known Gauss–Bonnet–Chern theorem for a compact Riemannian manifold with boundary.The boundary integrand is obtained by carefully analyzing the asymptotic behavior of the boundary local time of RBM for small times.
基金supported by National Science Foundation of USA(Grant No.DMS-1206276)National Natural Science Foundation of China(Grant No.11601280)
文摘In this paper, we investigate Markovian backward stochastic differential equations(BSDEs) with the generator and the terminal value that depend on the solutions of stochastic differential equations with rankbased drift coefficients. We study regularity properties of the solutions of this kind of BSDEs and establish their connection with semi-linear backward parabolic partial differential equations in simplex with Neumann boundary condition. As an application, we study the European option pricing problem with capital size based stock prices.
基金Supported by the National Natural Science Foundation of China (No.10371053,10971249)
文摘In Internet environment, traffic flow to a link is typically modeled by superposition of ON/OFF based sources. During each ON-period for a particular source, packets arrive according to a Poisson process and packet sizes (hence service times) can be generally distributed. In this paper, we establish heavy traffic limit theorems to provide suitable approximations for the system under first-in first-out (FIFO) and work-conserving service discipline, which state that, when the lengths of both ON- and OFF-periods are lightly tailed, the sequences of the scaled queue length and workload processes converge weakly to short-range dependent reflecting Gaussian processes, and when the lengths of ON- and/or OFF-periods are heavily tailed with infinite variance, the sequences converge weakly to either reflecting fractional Brownian motions (FBMs) or certain type of long- range dependent reflecting Gaussian processes depending on the choice of scaling as the number of superposed sources tends to infinity. Moreover, the sequences exhibit a state space collapse-like property when the number of sources is large enough, which is a kind of extension of the well-known Little's law for M/M/1 queueing system. Theory to justify the approximations is based on appropriate heavy traffic conditions which essentially mean that the service rate closely approaches the arrival rate when the number of input sources tends to infinity.
基金Supported by the Fundamental Research Funds for the Central Universities (BUPT 2009RC0707) and National Natural Science Foundation of China (Grant No. 10901023)
文摘This paper studies a multitype re-entrant line under smaller-buffer-first-served policy, which is an extension of first-buffer-first-served re-entrant line. We prove a heavy traffic limit theorem. The key to the proof is to prove the uniform convergence of the corresponding critical fluid model.
文摘In this paper, we define a class of domains in R^n. Using the synchronous coupling of reflecting Brownian motion, we obtain the monotonicity property of the solution of the heat equation with the Neumann boundary conditions. We then show that the hot spots conjecture holds for this class of domains.