Stochastic Burgers PDEs with random coefficients and a generalization of the Cole–Hopf transformation

Nikolaos Englezos (), Nikolaos E. Frangos, Xanthi-Isidora Kartala and Athanasios N. Yannacopoulos

Stochastic Processes and their Applications, 2013, vol. 123, issue 8, 3239-3272

Abstract: This paper studies forward and backward versions of the random Burgers equation (RBE) with stochastic coefficients. First, the celebrated Cole–Hopf transformation reduces the forward RBE to a forward random heat equation (RHE) that can be treated pathwise. Next we provide a connection between the backward Burgers equation and a system of FBSDEs. Exploiting this connection, we derive a generalization of the Cole–Hopf transformation which links the backward RBE with the backward RHE and investigate the range of its applicability. Stochastic Feynman–Kac representations for the solutions are provided. Explicit solutions are constructed and applications in stochastic control and mathematical finance are discussed.

Keywords: Stochastic Burgers equation; Random coefficients; Generalized Cole–Hopf transformation; Stochastic heat equation; Stochastic Feynman–Kac formulas; Controllability; Contingent claim pricing (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:8:p:3239-3272

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DOI: 10.1016/j.spa.2013.03.001

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