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The trace of a one-dimensional Markov process with Lévy measure

✍ Scribed by Heidrun Seidel

Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
565 KB
Volume
97
Category
Article
ISSN
0025-584X

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✦ Synopsis

The trace of a one-dimensional MARHOV process with LBVY measure By HEIDRUN SEIDEL of Dresden (Eingegangen am 10. 10. 1979) Q 1. Introduction Let X = ( X t , X t , P,) be a right-continuous FELLER process on the interval [O, I] with infinitesimal generator $ of the form (1.1) gm:, = D,DJ(x) + b ( 4 f'(4 0 Here m is a continuous, strongly increasing function on [O, I], and D,D, denotes a generalized second order differential operator as defined e.g. in [6] or [7]. The functions y,(xE[O, 11) are given by v,(y):= Y (y-s) dm(s).

5

The domain %(g) of the operator g is supposed to consist of those fC% (D,D,) which satisfy two boundary conditions of Feller-Ventcel-type :

0 with nonnegative constants xo, x i , no, and nl, and finite nonnegative measures qo on (0, I], qi on [ O , I ) , such that the following conditions are fulfilled: 0;o

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