Derivative Formula and Gradient Estimates for Gruschin Type Semigroups

Feng-Yu Wang ()
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Feng-Yu Wang: Beijing Normal University

Journal of Theoretical Probability, 2014, vol. 27, issue 1, 80-95

Abstract: Abstract By solving a control problem and using Malliavin calculus, an explicit derivative formula is derived for the semigroup P t generated by the Gruschin type operator on ℝ m ×ℝ d : where σ∈C 1(ℝ m ;ℝ d ⊗ℝ d ) might be degenerate. In particular, if σ(x) is comparable with |x| l I d×d for some l≥1 in the sense of (1.5), then for any p>1 there exists a constant C p >0 such that which implies a new Harnack type inequality for the semigroup. A more general model is also investigated.

Keywords: Gruschin semigroup; Derivative formula; Gradient estimate; 60J75; 60J45 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10959-012-0427-2

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