JOINT H?LDER CONTINUITY OF PARABOLIC ANDERSON MODEL

We obtain the H?lder continuity and joint H?lder continuity in space and time for the random field solution to the parabolic Anderson equation ■ in d-dimensional space, where ■ is a mean zero Gaussian noise with temporal covariance γ0 and spatial covariance given by a spectral density μ(ξ). We assume that ■ and ■ , where αi, i = 1, ···, d(or α) can take negative value.     

Exact maximum likelihood estimator for drift fractional Brownian motion at discrete observation

This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.     

CONVERGENCE RATE OF AN APPROXIMATION TO MULTIPLE INTEGRAL OF FBM

In this article, we study the rate of convergence of the polygonal approximation to multiple stochastic integral Sp （f） of fractional Brownian motion of Hurst parameter H 〈 1/2 when the fractional Brownian motion is replaced by its polygonal approximation. Under different conditions on f and for different p, we obtain different rates.     

基空间上的随机泛函的随机分析

设(Ω,P)是一个概率空间,T=[O,T]是一个时间区间,F:T×Ω→R~d是一个参数在T中的随机变量族。K.Ito的随机GalcuZlus讨论的是F对时间的依赖性(c.f.[8])。但是,关于样本的依赖性的分析近来愈来愈受到重视,尤其是Malliavin的Calculus的出现,及其在许多领域中找到了它的应     

SOME NOTES ON MULTIPLE STRA TONOVITCH INTEGRALES

Tn this paper we point out some similarities of multiple Stratonovitch integrale series with Talor series and prove some properties and a convergence theorem.     

SYMMETRIC INTEGRAL AND THE APPROXIMATION THEOREM OF STOCHASTIC INTEGRAL IN THE PLANE

In this paper, we consider the approximation problem of stochastic integral with respect to two-parameter Wiener process. We first introduce a kind of symmetric integral and prove it obeys the chain rule. Then we apply an integral formula of bounded variation functions with two variables to show the approximation theorem of stochastic integral in the plane. In particular, we prove that the symmetric stochastic integral is stable when the limit is taken in the sense of L~2convergence.     

MULTI-DIMENSIONAL GEOMETRIC BROWNIAN MOTIONS, ONSAGER-MACHLUP FUNCTIONS, AND APPLICATIONS TO MATHEMATICAL FINANCE

1 IntroductionThe solution of the following stochastic differential equationis called the geometric Brownian motion, where a(t), b(t) are deterministic functions of ti ac isa Brownian motion, and ddt is the It6 integral. This equation has been successfully applied tothe financial problems such as modeling the prices of stocks, sc.e for example, [81, [7], [14], [13],[19], [21]. When the initial condition is given, i.e. xo = x, the solution isIt is known that in the financial market, it is als…     

A RANDOM TRANSPORT-DIFFUSION EQUATION

In this paper we study the integral curve in a random vector field perturbed by white noise. It is related to a stochastic transport-diffusion equation. Under some conditions on the covariance function of the vector field, the solution of this stochastic partial differential equation is proved to have moments. The exact p-th moment is represented through integrals with respect to Brownian motions. The basic tool is Girsanov formula.     

ON THE NECESSARY AND SUFFICIENT CONDITIONS TO SOLVE A HEAT EQUATION WITH GENERAL ADDITIVE GAUSSIAN NOISE

In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two different methods, respectively, based on variance computations and on path-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution.     

An enlargement of filtration for Brownian motion

Let Bt be an Ft Brownian motion and Gt be an enlargement of filtration of Ft from some Gaussian random variables. We obtain equations for ht such that Bt ht is a Gt-Brownian motion.