## Abstract

In this article, the existence of a unique solution in the variational approach of the stochastic evolution equation

$$\dX(t) = F(X(t)) \dt + G(X(t)) \dL(t)$$

driven by a cylindrical Lévy process L is established. The coefficients F and G are assumed to satisfy the usual monotonicity and coercivity conditions. The noise is modelled by a cylindrical Lévy processes which is assumed to belong to a certain subclass of cylindrical Lévy processes and may not have finite moments.

$$\dX(t) = F(X(t)) \dt + G(X(t)) \dL(t)$$

driven by a cylindrical Lévy process L is established. The coefficients F and G are assumed to satisfy the usual monotonicity and coercivity conditions. The noise is modelled by a cylindrical Lévy processes which is assumed to belong to a certain subclass of cylindrical Lévy processes and may not have finite moments.

Original language | English |
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Number of pages | 20 |

Journal | Discrete and continuous dynamical systems-Series b |

Publication status | Accepted/In press - 24 Apr 2020 |

## Keywords

- cylindrical Lévy processes
- stochastic partial differential equations
- multiplicative noise
- variational solutions
- Stochastic integration