The stochastic Cauchy problem driven by a cylindrical Lévy process

TY - JOUR

T1 - The stochastic Cauchy problem driven by a cylindrical Lévy process

AU - Kumar, Umesh

AU - Riedle, Markus

PY - 2020/1

Y1 - 2020/1

N2 - In this work, we derive sufficient and necessary conditions for the existence of a weak and mild solution of an abstract stochastic Cauchy problem driven by an arbitrary cylindrical Lévy process. Our approach requires to establish a stochastic Fubini result for stochastic integrals with respect to cylindrical Lévy processes. This approach enables us to conclude that the solution process has almost surely scalarly square integrable paths. Further properties of the solution such as the Markov property and stochastic continuity are derived.

AB - In this work, we derive sufficient and necessary conditions for the existence of a weak and mild solution of an abstract stochastic Cauchy problem driven by an arbitrary cylindrical Lévy process. Our approach requires to establish a stochastic Fubini result for stochastic integrals with respect to cylindrical Lévy processes. This approach enables us to conclude that the solution process has almost surely scalarly square integrable paths. Further properties of the solution such as the Markov property and stochastic continuity are derived.

KW - Cauchy problem

KW - Cylindrical Lévy process

KW - Cylindrical infinitely divisible

KW - Stochastic Fubini theorem

UR - https://arxiv.org/abs/1803.04365

UR - http://www.scopus.com/inward/record.url?scp=85079464866&partnerID=8YFLogxK

U2 - 10.1214/19-EJP407

DO - 10.1214/19-EJP407

M3 - Article

SN - 1083-6489

VL - 25

SP - 1

EP - 26

JO - Electronic Journal Of Probability

JF - Electronic Journal Of Probability

IS - 10

M1 - 10

ER -