Research output: Contribution to journal › Article

**Variational solutions of stochastic partial differential equations with cylindrical Lévy noise.** / Kosmala, Tomasz; Riedle, Markus.

Research output: Contribution to journal › Article

Kosmala, T & Riedle, M 2020, 'Variational solutions of stochastic partial differential equations with cylindrical Lévy noise', *Discrete and continuous dynamical systems-Series b*.

Kosmala, T., & Riedle, M. (Accepted/In press). Variational solutions of stochastic partial differential equations with cylindrical Lévy noise. *Discrete and continuous dynamical systems-Series b*.

Kosmala T, Riedle M. Variational solutions of stochastic partial differential equations with cylindrical Lévy noise. Discrete and continuous dynamical systems-Series b. 2020 Apr 24.

@article{d498f99a0d564588a8e57156773ce753,

title = "Variational solutions of stochastic partial differential equations with cylindrical L{\'e}vy noise",

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 L{\'e}vy 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 L{\'e}vy processes which is assumed to belong to a certain subclass of cylindrical L{\'e}vy processes and may not have finite moments. ",

keywords = "cylindrical L{\'e}vy processes, stochastic partial differential equations, multiplicative noise, variational solutions, Stochastic integration",

author = "Tomasz Kosmala and Markus Riedle",

note = "AMS 2010 Subject Classification: 60H15, 60G51, 60G20, 28A35",

year = "2020",

month = apr,

day = "24",

language = "English",

journal = "Discrete and continuous dynamical systems-Series b",

issn = "1531-3492",

publisher = "Southwest Missouri State University",

}

TY - JOUR

T1 - Variational solutions of stochastic partial differential equations with cylindrical Lévy noise

AU - Kosmala, Tomasz

AU - Riedle, Markus

N1 - AMS 2010 Subject Classification: 60H15, 60G51, 60G20, 28A35

PY - 2020/4/24

Y1 - 2020/4/24

N2 - 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.

AB - 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.

KW - cylindrical Lévy processes

KW - stochastic partial differential equations

KW - multiplicative noise

KW - variational solutions

KW - Stochastic integration

UR - https://arxiv.org/abs/1807.11418

M3 - Article

JO - Discrete and continuous dynamical systems-Series b

JF - Discrete and continuous dynamical systems-Series b

SN - 1531-3492

ER -

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