Functionals Associated with Gradient Stochastic Flows and Nonlinear SPDEs

B. Iftimie (), M. Marinescu and C. Vârsan ()
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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”

Chapter Chapter 15 in Advanced Mathematical Methods for Finance, 2011, pp 397-415 from Springer

Abstract: 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.

Keywords: Stochastic partial differential equations; Fisk–Stratonovich stochastic integral; Stochastic flow; Gradient representation; Hamilton–Jacobi equations; 60H15; 60H30; 35F20; 35Q35 (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18412-3_15

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DOI: 10.1007/978-3-642-18412-3_15

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