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Functionals Associated with Gradient Stochastic Flows and Nonlinear SPDEs

In: Advanced Mathematical Methods for Finance

Author

Listed:
  • B. Iftimie

    (Academy of Economic Sciences, Department of Mathematics)

  • M. Marinescu

    (Academy of Economic Sciences, Department of Mathematics)

  • C. Vârsan

    (Institute of Mathematics of the Romanian Academy “Simion Stoilow”)

Abstract

In this paper we construct and provide a representation for a classical solution of some nonlinear SPDE driven by Fisk–Stratonovich stochastic integral. Our main assumption is the commuting property of the drift and diffusion vector fields with respect to the usual Lie bracket. This result is next applied for a system of Burgers equations with stochastic perturbations and also to the computations of some expectations of functionals depending on the final value of some non-Markovian process.

Suggested Citation

  • B. Iftimie & M. Marinescu & C. Vârsan, 2011. "Functionals Associated with Gradient Stochastic Flows and Nonlinear SPDEs," Springer Books, in: Giulia Di Nunno & Bernt Øksendal (ed.), Advanced Mathematical Methods for Finance, chapter 0, pages 397-415, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18412-3_15
    DOI: 10.1007/978-3-642-18412-3_15
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