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- Title
Stochastic equations with multidimensional drift driven by Levy processes.
- Authors
Kurenok, V. P.
- Abstract
The stochastic equation dXt = dLt + a(t, Xt)dt, t ≥ 0, is considered where L is a d-dimensional Levy process with the characteristic exponent ψ(ξ), ξ ∈ Bbb R, d ≥ 1. We prove the existence of (weak) solutions for a bounded, measurable coefficient a and any initial value X0 = x0 ∈ Rd when (Re ψ(ξ))-1 = o(|ξ|-1) as |ξ| → ∞. The proof idea is based on Krylov's estimates for Levy processes with time-dependent drift and some variants of those estimates are derived in this note.
- Subjects
STOCHASTIC processes; STOCHASTIC analysis; NUMERICAL solutions to equations; LEVY processes; ESTIMATES
- Publication
Random Operators & Stochastic Equations, 2006, Vol 14, Issue 4, p311
- ISSN
0926-6364
- Publication type
Article
- DOI
10.1515/156939706779801705