Existence and uniqueness of path wise solutions for stochastic integral equations driven by Lévy noise on separable Banach spaces

DOI10.1080/17442500600813140zbMath1119.60040OpenAlexW2081359578MaRDI QIDQ3426281

Vidyadhar Mandrekar, Barbara Rüdiger

Publication date: 8 March 2007

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17442500600813140

zbMATH Keywords

stochastic differential equationLévy processmartingale measurecompensated Poisson random measureM-type 2 Banach spacestochastic integral on separable Banach space

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Stochastic integrals (60H05) Probabilistic methods in Banach space theory (46B09) Random measures (60G57) Integral, integro-differential, and pseudodifferential operators (47G99)

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The existence and uniqueness of mild solutions to stochastic differential equations with Lévy noise ⋮ The existence and asymptotic behaviour of energy solutions to stochastic age-dependent population equations driven by Levy processes ⋮ Maximal regularity for stochastic convolutions driven by Lévy processes ⋮ Stochastic reaction-diffusion equations driven by jump processes ⋮ Stochastic non-resistive magnetohydrodynamic system with Lévy noise ⋮ Strong solutions of stochastic models for viscoelastic flows of Oldroyd type ⋮ Some refinements of existence results for SPDEs driven by Wiener processes and Poisson random measures ⋮ Shell model of turbulence perturbed by Lévy noise ⋮ Poisson stable solutions for stochastic PDEs driven by Lévy noise ⋮ The existence and asymptotic behaviour of energy solutions to stochastic 2D functional Navier-Stokes equations driven by Lévy processes ⋮ Foundations of the theory of semilinear stochastic partial differential equations ⋮ Uniqueness of invariant measures of infinite dimensional stochastic differential equations driven by Lévy noises ⋮ Strong solutions for SPDE with locally monotone coefficients driven by Lévy noise ⋮ Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Lévy noise ⋮ Well-posedness of Hall-magnetohydrodynamics system forced by Lévy noise ⋮ Stochastic Euler equations of fluid dynamics with Lévy noise ⋮ Itô formula for stochastic integrals w.r.t. compensated Poisson random measures on separable Banach spaces

Cites Work

• Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Lévy noise
• Martingales with values in uniformly convex spaces
• Parabolic SPDEs driven by Poisson white noise
• Itô formula for stochastic integrals w.r.t. compensated Poisson random measures on separable Banach spaces
• Stochastic integration with respect to compensated Poisson random measures on separable Banach spaces
• Lévy Processes and Stochastic Calculus
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