Let{W1（t）, t∈R＋} and {W2（t）, t∈R＋} be two independent Brownian motions with W1（0） = W2（0） = 0. {H （t） = W1（｜W2（t）｜）, t ∈R＋} is called a generalized iterated Brownian motion. In this paper, the Ha...Let{W1（t）, t∈R＋} and {W2（t）, t∈R＋} be two independent Brownian motions with W1（0） = W2（0） = 0. {H （t） = W1（｜W2（t）｜）, t ∈R＋} is called a generalized iterated Brownian motion. In this paper, the Hausdorff dimension and packing dimension of the level sets {t ∈[0, T ], H（t） = x} are established for any 0 T ≤ 1.展开更多
Let {W (t), t ∈ R}, {B(t), t ∈ R +} be two independent Brownian motions on R with W(0) = B(0) = 0. In this paper, we shall consider the exact Hausdorff measures for the image and graph sets of the d-dimensional iter...Let {W (t), t ∈ R}, {B(t), t ∈ R +} be two independent Brownian motions on R with W(0) = B(0) = 0. In this paper, we shall consider the exact Hausdorff measures for the image and graph sets of the d-dimensional iterated Brownian motion X(t), where X(t) = (X 1(t),…, X d (t)) and X 1(t),…, X d (t) are d independent copies of Y(t) = W(B(t)). In particular, for any Borel set Q ? (0, ∞), the exact Hausdorff measures of the image X(Q) = {X(t): t ∈ Q} and the graph GrX(Q) = {(t, X(t)): t ∈ Q} are established.展开更多
In this paper we construct models obtained by suitably combining Brownian motions and telegraphs in such a way that their transition functions satisfy higher-order parabolic or hyperbolic equations of different types....In this paper we construct models obtained by suitably combining Brownian motions and telegraphs in such a way that their transition functions satisfy higher-order parabolic or hyperbolic equations of different types. Equations with time-varying coefficients are also derived by considering processes endowed either with drift or with suitable modifications of their structure. Finally the distribution of the maximum of the iterated Brownian motion (along with some other properties) is presented.展开更多
基金Supported by the National Science Foundation of Zhejiang(No.LQ12F03003)
文摘Let{W1（t）, t∈R＋} and {W2（t）, t∈R＋} be two independent Brownian motions with W1（0） = W2（0） = 0. {H （t） = W1（｜W2（t）｜）, t ∈R＋} is called a generalized iterated Brownian motion. In this paper, the Hausdorff dimension and packing dimension of the level sets {t ∈[0, T ], H（t） = x} are established for any 0 T ≤ 1.
基金This work was partially supported by the National Natural Science Foundation of China (Grant No. 10131040)China Postdoctoral Science Foundation.
文摘Let {W (t), t ∈ R}, {B(t), t ∈ R +} be two independent Brownian motions on R with W(0) = B(0) = 0. In this paper, we shall consider the exact Hausdorff measures for the image and graph sets of the d-dimensional iterated Brownian motion X(t), where X(t) = (X 1(t),…, X d (t)) and X 1(t),…, X d (t) are d independent copies of Y(t) = W(B(t)). In particular, for any Borel set Q ? (0, ∞), the exact Hausdorff measures of the image X(Q) = {X(t): t ∈ Q} and the graph GrX(Q) = {(t, X(t)): t ∈ Q} are established.
基金This work is partially supported by the Natural Science Foundation of Guangdong ProvinceNational Natural Science Foundation of China grant No. 19501026the Alexander yon Humbodlt Foundation
文摘In this paper we construct models obtained by suitably combining Brownian motions and telegraphs in such a way that their transition functions satisfy higher-order parabolic or hyperbolic equations of different types. Equations with time-varying coefficients are also derived by considering processes endowed either with drift or with suitable modifications of their structure. Finally the distribution of the maximum of the iterated Brownian motion (along with some other properties) is presented.
