两参数的Tanaka型公式及其应用

本文用随机分析方法讨论两参数Wiener过程的局部时与自交局部时。作为它们的应用,还证明了形式测度的存在性,并且得到了单参数和两参数Wiener过程的水平集的Hausdorff维数。     

INFINITE DIMENSIONAL MALLIAVIN CALCULUS AND ITS APPLICATION

In this paper we study the infinite dimensional Malliavin calculus, and apply it to determingwhen the solution of an infinite dimensional stochastic differential equation has the property thatits finite dimensional distributions possess smooth density.     

AN INTERSECTION PROPERTY OF THE SIMPLE RANDOM WALKS IN Z~d

ＡＮＩＮＴＥＲＳＥＣＴＩＯＮＰＲＯＰＥＲＴＹＯＦＴＨＥＳＩＭＰＬＥＲＡＮＤＯＭＷＡＬＫＳＩＮＺ￣ｄＺＨＯＵＸＩＡＮＹＩＮ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＢｅｉｊｉｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ１００８７５，Ｃｈｉｎａ）Ａｂｓｔ...     

THE H(?)LDER CONTINUITY OF WESTWATER PROCESS AND ITS APPLICATIONS

In this paper, the Holder continuity of Westwater process X_t is concerned. More precisely,we show that there exists a random variable r_C∈(0,∞) for any C∈(3,∞) such that|X_s-X_t|≤C|(s-t)|~(1/2)|log|t-s||相似文献   

THE RANGE OF RANDOM WALK ON TREES AND RELATED TRAPPING PROBLEM

1.IntroductionLetTNbetheinfinitetreewithN 1branchesemanatingfromeachvertex.Namely,TNisaninfiniteconnectedgraphwithnonon-trivialclosedloopsinwhicheverynodebelongstoexactlyN Iedges.SinceTIcanbethoughtofasaonedimensionallattice,whichhasbeenwellstudied,throug…     

AN ASYMPTOTIC ESTIMATION OF THE MOMENTS FOR TWO-DIMENSIONAL POLYMER MEASURE

Let v_T (g) be the polymer measure in two dimensions and {w (t)} its coordinate process. This paper presents the following estimations: For any given g>0 and a>0, there exist constants C_1, C_2 ∈ (0, ∞) such that     

HAUSDORFF DIMENSION OF THE DOUBLE POINT SET OF THE WESTWATER PROCESS

Let X={X_i}_(t∈[0,1])be the Westwater process which is the coordinate process under3-dimensional polymer measure v(g)constructed by J.Westwater.In this paper,theHausdorff dimension problem for the double point set of X is investigated.As a result,it is proved thatdim D_2=1,v(g)-a.e.,where D_2={x∈R~3:X=X_(?)=x for some s相似文献   

APPLICATIONS OF MALLIAVIN CALCULUS TO STOCHASTIS DIFFERENTIAL EQUATIONS WITH TIME-DEPENDENT COEFFICIENTS

In this paper, we apply Malliavin calculus to discuss when the solutions of stochastic differen-tial equations (SDE's) with time-dependent coefficients have smooth density. Under Hormander'scondition,we conclude that the solutions of the SDE's have smooth density. As a consequence,we get the hypoellipticity for inhomogeneous differential operators.     

关于带跳随机微分方程解的密度光滑性

本文利用Malliavin随机变分来讨论一类带跳随机微分方程解的密度光滑性。在退化情形并且当跳部分为零时,所给的条件就是通常的H(?)rmander条件。     

A note on the asymptotics of the polymer measures in one dimension

Given g∈(0,∞), we prove thatfor some constant C∈(0,∞), where (g, T) is the polymer measure defined on C_0([0, T]→R~1), and {W(t)}t∈[0,T] is the corresponding coordinate process.