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V. P. Kurenok

Stochastic equations with multidimensional drift driven by Levy processes

Keywords: Multidimensional Levy processes, stochastic differential equations, time-dependent drift, weak convergence

The stochastic equation

dX_t = dL_t + a(t,X_t )dt, t > 0,

is considered where L is a d-dimensional Levy process with the characteristic exponent (ξ), ξ ∈ Bbb R, d > 1. We prove the existence of (weak) solutions for a bounded, measurable coefficient a and any initial value X ₀ = x ₀ ∈ when

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.

Random Operators and Stochastic Equations, Walter de Gruyter

Print ISSN: 0926-6364
Volume: 14, 12/2006
Pages: 311 - 324

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