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Statistics on crossings of discretized diffusions and local time

Florens, Danielle (1991), Statistics on crossings of discretized diffusions and local time, Stochastic Processes and their Applications, 39, 1, p. 139-151. http://dx.doi.org/10.1016/0304-4149(91)90038-E

Type
Article accepté pour publication ou publié
Date
1991
Journal name
Stochastic Processes and their Applications
Volume
39
Number
1
Publisher
Elsevier
Pages
139-151
Publication identifier
Metadata
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Author(s)
Florens, Danielle
Abstract (EN)
Let X̄Δ be the process obtained by linear interpolation from discrete observations of a diffusion X. In the first part of this paper we study the statistical properties of the observation sgn X̄Δ. In the second part we prove that the number of zero-crossings of X̄Δ, suitably normalized, converges in (L2-norm) to the zero local time of X.
Subjects / Keywords
diffusion; local time; crossings; estimation