Symmetrizations of Markov processes |
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Authors: | Joseph Glover Murali Rao |
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Institution: | (1) Department of Mathematics, University of Florida, 32611 Gainesville, Florida |
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Abstract: | Two methods for symmetrizing Markov processes are discussed. Letu
a(x, y) be the potential density of a Lévy process on a compact Abelian groupG. A general condition is given that guarantees thatv(x, y)=ua(x, y)+ua(y, x) is the potential density of a symmetric Lévy process onG. The second method arises by considering the linear space of one-potentialsU
1
f, withf inL
2, endowed with the inner product (U
1
f,U
1
g)=fU
1
g+gU
1
f. If the semigroup ofX(t) is normal, then the completionH of this space is the Dirichlet space of a symmetric processY(t). A set that is semipolar forX(t) is polar forY(t). |
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Keywords: | Markov process potential density symmetric Lé vy process compact Abelian group |
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