This paper gives a characterization of a Hunt process path by the first exit left limit distribution. It is also showed that if the first exit left limit distribution leaving any ball from the center is a uniform dist...This paper gives a characterization of a Hunt process path by the first exit left limit distribution. It is also showed that if the first exit left limit distribution leaving any ball from the center is a uniform distribution on the sphere, then the Levy Processes are a scaled Brownian motion.展开更多
In this paper, we prove that, under certain conditions, a strong law of large number holds for a class of branching particle systems X corresponding to the parameters （Y,β,φ）, where Y is a Hunt process and φ is t...In this paper, we prove that, under certain conditions, a strong law of large number holds for a class of branching particle systems X corresponding to the parameters （Y,β,φ）, where Y is a Hunt process and φ is the generating function for the offspring. The main tool of this paper is the spine decomposition and we only need an L log L condition.展开更多
Consider a supercritical superprocess X = {Xt, t 〉~ O} on a locally compact separable metric space （E, m）. Suppose that the spatial motion of X is a Hunt process satisfying certain conditions and that the branching...Consider a supercritical superprocess X = {Xt, t 〉~ O} on a locally compact separable metric space （E, m）. Suppose that the spatial motion of X is a Hunt process satisfying certain conditions and that the branching mechanism is of the form展开更多
We study a class of nonlocal-diffusion equations with drifts,and derive a priori-Hölder estimate for the solutions by using a purely probabilistic argument,whereis an intrinsic scaling function for the equation.
Risks embedded in asset price dynamics are taken to be accumulations of surprise jumps.A Markov pure jump model is formulated on making variance gamma parameters deterministic functions of the price level.Estimation i...Risks embedded in asset price dynamics are taken to be accumulations of surprise jumps.A Markov pure jump model is formulated on making variance gamma parameters deterministic functions of the price level.Estimation is done by matrix exponentiation of the transition rate matrix for a continuous time finite state Markov chain approximation.The motion is decomposed into a space dependent drift and a space dependent martingale component.Though there is some local mean reversion in the drift,space dependence of the martingale component renders the dynamics to be of the momentum type.Local risk is measured using market calibrated measure distortions that introduce risk charges into the lower and upper prices of two price economies.These risks are compensated by the exponential variation of space dependent arrival rates.Estimations are conducted for the S&P 500 index(SPX),the exchange traded fund for the financial sector(XLF),J.P.Morgan stock prices(JPM),the ratio of JPM to XLF,and the ratio of XLF to SPX.展开更多
基金Supported by the National Natural Science Foundation of China (10601047)
文摘This paper gives a characterization of a Hunt process path by the first exit left limit distribution. It is also showed that if the first exit left limit distribution leaving any ball from the center is a uniform distribution on the sphere, then the Levy Processes are a scaled Brownian motion.
文摘In this paper, we prove that, under certain conditions, a strong law of large number holds for a class of branching particle systems X corresponding to the parameters （Y,β,φ）, where Y is a Hunt process and φ is the generating function for the offspring. The main tool of this paper is the spine decomposition and we only need an L log L condition.
文摘Consider a supercritical superprocess X = {Xt, t 〉~ O} on a locally compact separable metric space （E, m）. Suppose that the spatial motion of X is a Hunt process satisfying certain conditions and that the branching mechanism is of the form
基金The research of ZC was partially supported by NSF Grant DMS-1206276.The research of XZ was partially supported by NSFC Grant of China(Nos.11271294,11325105).
文摘We study a class of nonlocal-diffusion equations with drifts,and derive a priori-Hölder estimate for the solutions by using a purely probabilistic argument,whereis an intrinsic scaling function for the equation.
文摘Risks embedded in asset price dynamics are taken to be accumulations of surprise jumps.A Markov pure jump model is formulated on making variance gamma parameters deterministic functions of the price level.Estimation is done by matrix exponentiation of the transition rate matrix for a continuous time finite state Markov chain approximation.The motion is decomposed into a space dependent drift and a space dependent martingale component.Though there is some local mean reversion in the drift,space dependence of the martingale component renders the dynamics to be of the momentum type.Local risk is measured using market calibrated measure distortions that introduce risk charges into the lower and upper prices of two price economies.These risks are compensated by the exponential variation of space dependent arrival rates.Estimations are conducted for the S&P 500 index(SPX),the exchange traded fund for the financial sector(XLF),J.P.Morgan stock prices(JPM),the ratio of JPM to XLF,and the ratio of XLF to SPX.
