Let Xt（x） be the solution of stochastic differential equations with smooth and bounded derivatives coefficients. Let Xnt （x） be the Euler discretization scheme of SDEs with step 2-n . In this note, we prove that f...Let Xt（x） be the solution of stochastic differential equations with smooth and bounded derivatives coefficients. Let Xnt （x） be the Euler discretization scheme of SDEs with step 2-n . In this note, we prove that for any R〉0 and γ∈（0, 1/2）, sup t∈[0,1],｜x｜≤R｜X nt （x,ω）-Xt （x,ω）｜≤ξR,γ（ω）2-nγ, n≥1, q.e., whereξR,γ（ω） is quasi-everywhere finite.展开更多
In this paper we prove a quasi-sure limit theorem of parabolic stochastic partial differential equations with smooth coefficients and some initial conditions,by the way,we obtain the quasi-sure continuity of the solut...In this paper we prove a quasi-sure limit theorem of parabolic stochastic partial differential equations with smooth coefficients and some initial conditions,by the way,we obtain the quasi-sure continuity of the solution.展开更多
In this paper, we prove that the process of product variation of a two-parameter smooth martingale admits an ∞ modification, which can be constructed as the quasi-sure limit of sum of the corresponding product variat...In this paper, we prove that the process of product variation of a two-parameter smooth martingale admits an ∞ modification, which can be constructed as the quasi-sure limit of sum of the corresponding product variation.展开更多
The authors construct a solution U_t(x) associated with a vector field on the Wiener space for all initial values except in a 1-slim set and obtain the 1-quasi-sure flow property where the vector field is a sum of a s...The authors construct a solution U_t(x) associated with a vector field on the Wiener space for all initial values except in a 1-slim set and obtain the 1-quasi-sure flow property where the vector field is a sum of a skew-adjoint operator not necessarily bounded and a nonlinear part with low regularity,namely one-fold differentiability.Besides,the equivalence of capacities under the transformations of the Wiener space induced by the solutions is obtained.展开更多
For a given Dirichlet series absolutely convergent and of order (R)p∈(o, +) in the right-halfplan, its terms can be multiplied respectively by the members of a suitable sequence defined ina probability or topological...For a given Dirichlet series absolutely convergent and of order (R)p∈(o, +) in the right-halfplan, its terms can be multiplied respectively by the members of a suitable sequence defined ina probability or topological space such that the series obtained is of order (R)ρ on any one ofcountably infinite horizontal haif lines almost or quasi surely.展开更多
Let X be a two parameter smooth semimartingale and (?) be its process of the product variation. It is proved that (?) can be approximated as D_∞-limit of sums of its discrete product variations as the mesh of divisio...Let X be a two parameter smooth semimartingale and (?) be its process of the product variation. It is proved that (?) can be approximated as D_∞-limit of sums of its discrete product variations as the mesh of division tends to zero. Moreover, this result can be strengthen to yield the quasi sure convergence of sums by estimating the speed of the convergence.展开更多
This paper investigates the problem of almost sure limit theorem for the maximum of quasi-stationary sequence based on the result of Turkman and Walker. We prove an almost sure limit theorem for the maximum of a class...This paper investigates the problem of almost sure limit theorem for the maximum of quasi-stationary sequence based on the result of Turkman and Walker. We prove an almost sure limit theorem for the maximum of a class of quasi-stationary sequence under weak dependence conditions of D （uk, un） and αtm,ln = 0 （（log log n）-（1＋ε））.展开更多
Large deviations for stochastic flow solutions to SDEs containing a small parameter are studied. The obtained results are applied to establish a Cp, r-large deviation principle for stochastic flows and for solutions t...Large deviations for stochastic flow solutions to SDEs containing a small parameter are studied. The obtained results are applied to establish a Cp, r-large deviation principle for stochastic flows and for solutions to anticipating SDEs. The recent results of Millet-Nualart-Sans and Yoshida are improved and refined.展开更多
文摘Let Xt（x） be the solution of stochastic differential equations with smooth and bounded derivatives coefficients. Let Xnt （x） be the Euler discretization scheme of SDEs with step 2-n . In this note, we prove that for any R〉0 and γ∈（0, 1/2）, sup t∈[0,1],｜x｜≤R｜X nt （x,ω）-Xt （x,ω）｜≤ξR,γ（ω）2-nγ, n≥1, q.e., whereξR,γ（ω） is quasi-everywhere finite.
基金This work is supported by NSF(No.10301011)of China and Project 973
文摘In this paper we prove a quasi-sure limit theorem of parabolic stochastic partial differential equations with smooth coefficients and some initial conditions,by the way,we obtain the quasi-sure continuity of the solution.
文摘In this paper, we prove that the process of product variation of a two-parameter smooth martingale admits an ∞ modification, which can be constructed as the quasi-sure limit of sum of the corresponding product variation.
基金Project supported by the National Natural Science Foundation of China(Nos.11171358,11026202,11101441)the Doctor Fund of Ministry of Education(Nos.20100171110038,20100171120041)the Natural Science Foundation of Guangdong Province(No.S2012040007458)
文摘The authors construct a solution U_t(x) associated with a vector field on the Wiener space for all initial values except in a 1-slim set and obtain the 1-quasi-sure flow property where the vector field is a sum of a skew-adjoint operator not necessarily bounded and a nonlinear part with low regularity,namely one-fold differentiability.Besides,the equivalence of capacities under the transformations of the Wiener space induced by the solutions is obtained.
文摘For a given Dirichlet series absolutely convergent and of order (R)p∈(o, +) in the right-halfplan, its terms can be multiplied respectively by the members of a suitable sequence defined ina probability or topological space such that the series obtained is of order (R)ρ on any one ofcountably infinite horizontal haif lines almost or quasi surely.
文摘Let X be a two parameter smooth semimartingale and (?) be its process of the product variation. It is proved that (?) can be approximated as D_∞-limit of sums of its discrete product variations as the mesh of division tends to zero. Moreover, this result can be strengthen to yield the quasi sure convergence of sums by estimating the speed of the convergence.
基金Project supported by the National Natural Science Foundation of China(11171275)the Natural Science Foundation Project of CQ(cstc2012jjA00029)Liaocheng University Foundation(X09005)
文摘This paper investigates the problem of almost sure limit theorem for the maximum of quasi-stationary sequence based on the result of Turkman and Walker. We prove an almost sure limit theorem for the maximum of a class of quasi-stationary sequence under weak dependence conditions of D （uk, un） and αtm,ln = 0 （（log log n）-（1＋ε））.
基金the National Natural Science Foundation of China (Grant No. 19971025) 973 Project.
文摘Large deviations for stochastic flow solutions to SDEs containing a small parameter are studied. The obtained results are applied to establish a Cp, r-large deviation principle for stochastic flows and for solutions to anticipating SDEs. The recent results of Millet-Nualart-Sans and Yoshida are improved and refined.
