On Markovian semigroups of Lévy driven SDEs, symbols and pseudo-differential operators
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- University of Sri Jayewardenepura
Abstract
We analyse analytic properties of nonlocal transition semigroups associated with a class of stochastic differential equations (SDEs) in Rd driven by pure jump–type Levy processes. First, we ´
will show under which conditions the semigroup will be analytic on the Besov space Bm
p,q(Rd)
with 1 ≤ p, q < ∞ and m ∈ R. Secondly, we present some applications by proving the strong
Feller property and give weak error estimates for approximating schemes of the SDEs over
the Besov space Bm
∞,∞(Rd). The choice of Besov spaces is twofold. First, observe that Besov
spaces can be defined via the Fourier transform and the partition of unity. Secondly, the space
of continuous functions can be characterised by Besov spaces.
Details
Original language | English |
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Pages (from-to) | 15-63 |
Number of pages | 49 |
Journal | Osaka journal of mathematics |
Volume | 59.2022 |
Issue number | 1 |
Publication status | Published - Jan 2022 |