Treats of dynamical systems with finite number of degrees of freedom such that the time evolution of the configuration variables for given initial conditions can well be described by controlled diffusions.Two suitable...Treats of dynamical systems with finite number of degrees of freedom such that the time evolution of the configuration variables for given initial conditions can well be described by controlled diffusions.Two suitable forms of stochastic action associated with the controlled diffusions are introduced in the general framework of stochastic control theory.By discretizing the stochastic action,the dynamical equations for the controlled diffusions of the given systems are derived in terms of generalized coordinates.These equations,together with the continuity equation,describe exactly the probability approach of the diffusion motion.展开更多
The aim of this article is to discuss a volume nullification property of thediffusion process determined by a stochastic differential equation on a manifold. LetX_t(x) be a diffusion process describing a flow of diffe...The aim of this article is to discuss a volume nullification property of thediffusion process determined by a stochastic differential equation on a manifold. LetX_t(x) be a diffusion process describing a flow of diffeomorphisms x→X_t (x) in a manifoldM, and K be a compact surface in M with positive finite Hausdorff measure. We presentconditions under which the area of X_t(K) goes to zero almost surely and in momentsas t→∞! in particular, the flow X_t(·) asymptotic nullifies the arc-lenth of orientedrectifiable arcs r: [0, 1]→M.展开更多
In this paper, we investigate super-uniformly elliptic diffusions {Xt,t ≥ 0} with its branching mechanism given by ψ(z) = γz1+β(0 < ≤ 1), and, when the initial value X0(dx) is one kind of invariant measures of...In this paper, we investigate super-uniformly elliptic diffusions {Xt,t ≥ 0} with its branching mechanism given by ψ(z) = γz1+β(0 < ≤ 1), and, when the initial value X0(dx) is one kind of invariant measures of the underlying processes, we show that if dimension d satisfies βd ≤ 2, then the random measures Xt will converge to the null in distribution and if βd > 2, then Xt will converge to a nondegenerative random measure in the same sense.展开更多
For a given probability density function p（x） on R^d, we construct a （non-stationary） diffusion process xt, starting at any point x in R^d, such that 1/T ∫_o^T δ（xt-x）dt converges to p（x） almost surely. The ...For a given probability density function p（x） on R^d, we construct a （non-stationary） diffusion process xt, starting at any point x in R^d, such that 1/T ∫_o^T δ（xt-x）dt converges to p（x） almost surely. The rate of this convergence is also investigated. To find this rate, we mainly use the Clark-Ocone formula from Malliavin calculus and the Girsanov transformation technique.展开更多
This paper examines the term structure of interest rate empirically, and discovers that jump-diffusion process is better than pure diffusion process when describing the stochastic behavior of interest rate, which incl...This paper examines the term structure of interest rate empirically, and discovers that jump-diffusion process is better than pure diffusion process when describing the stochastic behavior of interest rate, which including jump risk. Using two-stage method to estimate the term structure of China government bond market. Fitting the initial term structure with B-spline approximation method, and then as input to jump-diffusion model parameter estimation. The result accounts for that term structure with jump can explain the actual conditions of China government bond market.展开更多
文摘Treats of dynamical systems with finite number of degrees of freedom such that the time evolution of the configuration variables for given initial conditions can well be described by controlled diffusions.Two suitable forms of stochastic action associated with the controlled diffusions are introduced in the general framework of stochastic control theory.By discretizing the stochastic action,the dynamical equations for the controlled diffusions of the given systems are derived in terms of generalized coordinates.These equations,together with the continuity equation,describe exactly the probability approach of the diffusion motion.
基金Supported by the key Project of Chinese Minstry of Education and Supported by Natural Science Foundation of Beijing(1022004)
文摘The aim of this article is to discuss a volume nullification property of thediffusion process determined by a stochastic differential equation on a manifold. LetX_t(x) be a diffusion process describing a flow of diffeomorphisms x→X_t (x) in a manifoldM, and K be a compact surface in M with positive finite Hausdorff measure. We presentconditions under which the area of X_t(K) goes to zero almost surely and in momentsas t→∞! in particular, the flow X_t(·) asymptotic nullifies the arc-lenth of orientedrectifiable arcs r: [0, 1]→M.
文摘In this paper, we investigate super-uniformly elliptic diffusions {Xt,t ≥ 0} with its branching mechanism given by ψ(z) = γz1+β(0 < ≤ 1), and, when the initial value X0(dx) is one kind of invariant measures of the underlying processes, we show that if dimension d satisfies βd ≤ 2, then the random measures Xt will converge to the null in distribution and if βd > 2, then Xt will converge to a nondegenerative random measure in the same sense.
基金supported by the Simons Foundation (Grant No. 209206)a General Research Fund of the University of Kansas
文摘For a given probability density function p（x） on R^d, we construct a （non-stationary） diffusion process xt, starting at any point x in R^d, such that 1/T ∫_o^T δ（xt-x）dt converges to p（x） almost surely. The rate of this convergence is also investigated. To find this rate, we mainly use the Clark-Ocone formula from Malliavin calculus and the Girsanov transformation technique.
文摘This paper examines the term structure of interest rate empirically, and discovers that jump-diffusion process is better than pure diffusion process when describing the stochastic behavior of interest rate, which including jump risk. Using two-stage method to estimate the term structure of China government bond market. Fitting the initial term structure with B-spline approximation method, and then as input to jump-diffusion model parameter estimation. The result accounts for that term structure with jump can explain the actual conditions of China government bond market.
