Proves that Lévy-driven linear equations p(D)s = q(D)ḊL admit measurable solutions in Besov spaces and that semilinear versions p(D)u = g(·,u) + ḊL have measurable solutions in weighted Besov spaces when g is Lipschitz.
L\'{e}vy driven CARMA generalized processes and stochastic partial differential equations
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We give a new definition of a L\'{e}vy driven CARMA random field, defining it as a generalized solution of a stochastic partial differential equation (SPDE). Furthermore, we give sufficient conditions for the existence of a mild solution of our SPDE. Our model finds a connection between all known definitions of CARMA random fields, and especially for dimension 1 we obtain the classical CARMA process.
fields
math.PR 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
L\'{e}vy driven linear and semilinear stochastic partial differential equations
Proves that Lévy-driven linear equations p(D)s = q(D)ḊL admit measurable solutions in Besov spaces and that semilinear versions p(D)u = g(·,u) + ḊL have measurable solutions in weighted Besov spaces when g is Lipschitz.