Regularity of Ornstein-Uhlenbeck Processes Driven by a Lévy White Noise

TY - JOUR

T1 - Regularity of Ornstein-Uhlenbeck Processes Driven by a Lévy White Noise

AU - Brzezniak, Zdzisaw

AU - Zabczyk, Jerzy

PY - 2010/2

Y1 - 2010/2

N2 - The paper is concerned with spatial and time regularity of solutions to linear stochastic evolution equation perturbed by L,vy white noise "obtained by subordination of a Gaussian white noise". Sufficient conditions for spatial continuity are derived. It is also shown that solutions do not have in general cadlag modifications. General results are applied to equations with fractional Laplacian. Applications to Burgers stochastic equations are considered as well.

AB - The paper is concerned with spatial and time regularity of solutions to linear stochastic evolution equation perturbed by L,vy white noise "obtained by subordination of a Gaussian white noise". Sufficient conditions for spatial continuity are derived. It is also shown that solutions do not have in general cadlag modifications. General results are applied to equations with fractional Laplacian. Applications to Burgers stochastic equations are considered as well.

KW - Levy white noise

KW - Subordinator process

KW - Langevin equation

KW - Space regularity

KW - Stochastic heat equation

KW - Non-cadlag trajectories

KW - Stochastic Burgers equation

KW - GENERALIZED MEHLER SEMIGROUPS

KW - BANACH-SPACES

KW - STOCHASTIC CONVOLUTIONS

KW - EVOLUTION-EQUATIONS

KW - LEVY NOISE

KW - CONTINUITY

UR - http://www.scopus.com/inward/record.url?scp=77649238797&partnerID=8YFLogxK

U2 - 10.1007/s11118-009-9149-1

DO - 10.1007/s11118-009-9149-1

M3 - Article

SN - 0926-2601

VL - 32

SP - 153

EP - 188

JO - Potential analysis

JF - Potential analysis

IS - 2

ER -