Stochastic Volterra Equations in Banach Spaces and Stochastic Partial Differential Equations

By Xicheng Zhang. 2008

146 citations recorded by the source corpus.

In this paper, we first study the existence-uniqueness and large deviation estimate of solutions for stochastic Volterra integral equations with singular kernels in 2-smooth Banach spaces. Then, we apply them to a large class of semilinear stochastic partial differential equations (SPDE) driven by Brownian motions as well as by fractional Brownian motions, and obtain the existence of unique maximal strong solutions (in the sense of SDE and PDE) under local Lipschitz conditions. Lastly, high order SPDEs in a bounded domain of Euclidean space, second order SPDEs on complete Riemannian manifolds, as well as stochastic Navier-Stokes equations are investigated.

Subfields: Applied Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/a8037a5f1ac966fcaef59565ab71da092c47992b

How researchers see this paper

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In Applied Mathematics

1. Eduardo Abi Jaber
2. Sergio Pulido
3. Martin Larsson

In Control and Systems Engineering

1. Eduardo Abi Jaber
2. Sergio Pulido
3. Martin Larsson

In Finance

1. Eduardo Abi Jaber
2. Sergio Pulido
3. Martin Larsson
4. Christa Cuchiero
5. Omar El Euch

Citations in the corpus

• Affine Volterra processes (2017, background): “Stochastic Volterra equations have been studied by numerous authors; see e.g. Berger and Mizel (1980a,b); Protter (1985); Pardoux and Protter (1990); Zhang (2010); Mytnik and Salisbury (2015) among many others.”