On the collision local time of sub-fractional Brownian motions

2010 ◽  
Vol 80 (5-6) ◽  
pp. 296-308 ◽  
Author(s):  
Litan Yan ◽  
Guangjun Shen
Keyword(s):  
Local Time ◽  
Brownian Motions ◽  
Fractional Brownian Motions ◽  
Collision Local Time

Collision Local Times and Measure-Valued Processes

1991 ◽  
Vol 43 (5) ◽  
pp. 897-938 ◽  
Author(s):  
Martin T. Barlow ◽  
Steven N. Evans ◽  
Edwin A. Perkins
Keyword(s):  
Local Time ◽  
Forthcoming Paper ◽  
Local Times ◽  
Independent Interest ◽  
Positive Probability ◽  
Point Interactions ◽  
Random Measures ◽  
Brownian Motions ◽  
Collision Local Time ◽  
Finite Measures

AbstractWe consider two independent Dawson-Watanabe super-Brownian motions, Y1 and Y2. These processes are diffusions taking values in the space of finite measures on ℝd. We show that if d ≤ 5 then with positive probability there exist times t such that the closed supports of intersect; whereas if d > 5 then no such intersections occur. For the case d ≤ 5, we construct a continuous, non-decreasing measure–valued process L(Y1, Y2), the collision local time, such that the measure defined by , is concentrated on the set of times and places at which intersections occur. We give a Tanaka-like semimartingale decomposition of L(Y1, Y2). We also extend these results to a certain class of coupled measurevalued processes. This extension will be important in a forthcoming paper where we use the tools developed here to construct coupled pairs of measure-valued diffusions with point interactions. In the course of our proofs we obtain smoothness results for the random measures that are uniform in t. These theorems use a nonstandard description of Yi and are of independent interest.

Moduli of continuity of the local time of a class of sub-fractional Brownian motions

2017 ◽  
Vol 25 (4) ◽  
Author(s):  
Mohamed Ait Ouahra ◽  
Raby Guerbaz
Keyword(s):  
Local Time ◽  
Similarity Index ◽  
The Self ◽  
Local Times ◽  
Moduli Of Continuity ◽  
Self Similarity ◽  
Brownian Motions ◽  
Fractional Brownian Motions ◽  
Sharp Estimates

AbstractThe aim of this paper is to establish sharp estimates for the moduli of continuity of the local time of a class of sub-fractional Brownian motions. We also investigate the continuity of their local times with respect to the self-similarity index.

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