Hong Qian et al 1998 J. Phys. A: Math. Gen. 31 L527 doi:10.1088/0305-4470/31/28/002
On two-dimensional fractional Brownian motion and fractional Brownian random field
Hong Qian
,
, Gary M Raymond and James B Bassingthwaighte
LETTER TO THE EDITOR
As a generalization of one-dimensional fractional Brownian motion (1dfBm), we introduce a class of two-dimensional, self-similar, strongly correlated random walks whose variance scales with power law 
. We report analytical results on the statistical size and shape, and segment distribution of its trajectory in the limit of large N. The relevance of these results to polymer theory is discussed. We also study the basic properties of a second generalization of 1dfBm, the two-dimensional fractional Brownian random field (2dfBrf). It is shown that the product of two 1dfBms is the only 2dfBrf which satisfies the self-similarity defined by Sinai.
- PACS
- MSC
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60J65 Brownian motion (See also 58J65)
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
- Subjects
- Dates
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Issue 28 (17 July 1998)
Received 25 March 1998, in final form 1 June 1998
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On two-dimensional fractional Brownian motion and fractional Brownian random field
Hong Qian et al 1998 J. Phys. A: Math. Gen. 31 L527
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