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Transition Density of a Reflected Symmetric Stable Lévy Process in an Orthant

Amites Dasgupta and S. Ramasubramanian
Lecture Notes-Monograph Series
Vol. 41, Probability, Statistics and Their Applications: Papers in Honor of Rabi Bhattacharya (2003), pp. 117-132
Stable URL: http://www.jstor.org/stable/4356211
Page Count: 16
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Transition Density of a Reflected Symmetric Stable Lévy Process in an Orthant
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Abstract

Let $\{Z^{(s,x)}(t)\colon t\geq s\}$ denote the reflected symmetric α-stable Lévy process in an orthant D (with nonconstant reflection field), starting at (s, x). For 1 < α < 2, 0 ≤ s < t, x ∈ D̄ it is shown that $Z^{(s,x)}(t)$ has a probability density function which is continuous away from the boundary, and a representation given.

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