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Stochastic equations with multidimensional drift driven by Levy processes
-
V. P. Kurenok
Published/Copyright:
December 1, 2006
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 
(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 ∈ 
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.
Key Words: Multidimensional Levy processes,; stochastic differential equations,; time-dependent drift,; Krylov's estimates,; weak convergence.
Published Online: 2006-12-01
Published in Print: 2006-12-01
Copyright 2006, Walter de Gruyter
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Keywords for this article
Multidimensional Levy processes,;
stochastic differential equations,;
time-dependent drift,;
Krylov's estimates,;
weak convergence.
Articles in the same Issue
- Comparative stationarity of stochastic exponential and monomial densities
- Stochastic equations with multidimensional drift driven by Levy processes
- On existence of a solution for differential equation with interaction
- Regularity conditions and the maximum likelihood estimation in dynamical systems with small fractional Brownian noise
- On a generalized BSDE involving local time and application to a PDE with nonlinear boundary condition
- Limiting distribution of random motion in a n-dimensional parallelepiped
- Long-range dependence of time series for MSFT data of the prices of shares and returns
