TY - JOUR
T1 - Tanaka formulae for (α, d, β)-superprocesses
AU - Mytnik, Leonid
AU - Xiang, K. N.
N1 - Funding Information:
The authors thank an anonymous referee for comments and suggestions which improved the exposition. The second author would like to express his gratitude for the opportunity to spend some time as a postdoctoral fellow at the Technion (Israel) where this research was partially done. The research of L.M. was supported in part by a Grant from the GIF Young Scientists’ Program BSF and ISF. The research of K.-N.X. was supported in part by Chinese National Natural Science Foundation (Grant No. 10101002).
PY - 2004/4
Y1 - 2004/4
N2 - We establish Tanaka like formulae for the local time of (α, d, β)-superprocess in the dimensions where the local time exists. The result generalizes the result of Adler, Lewin who proved existence of Tanaka formulae for a class of super-processes with finite variance. The fact that we abandon the finite variance assumption, requires using an L1+θ convergence argument (with 0 < θ < β ≤ 1) rather than L 2 convergence, for the derivation of the Tanaka formulae.
AB - We establish Tanaka like formulae for the local time of (α, d, β)-superprocess in the dimensions where the local time exists. The result generalizes the result of Adler, Lewin who proved existence of Tanaka formulae for a class of super-processes with finite variance. The fact that we abandon the finite variance assumption, requires using an L1+θ convergence argument (with 0 < θ < β ≤ 1) rather than L 2 convergence, for the derivation of the Tanaka formulae.
KW - (α, d, β)-superprocess
KW - Local time
KW - Tanaka formula
UR - http://www.scopus.com/inward/record.url?scp=4043080488&partnerID=8YFLogxK
U2 - 10.1023/B:JOTP.0000020704.68569.25
DO - 10.1023/B:JOTP.0000020704.68569.25
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AN - SCOPUS:4043080488
SN - 0894-9840
VL - 17
SP - 483
EP - 502
JO - Journal of Theoretical Probability
JF - Journal of Theoretical Probability
IS - 2
ER -