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

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  • Englezos, Nikolaos
  • Frangos, Nikolaos E.
  • Kartala, Xanthi-Isidora
  • Yannacopoulos, Athanasios N.

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.

Suggested Citation

  • Englezos, Nikolaos & Frangos, Nikolaos E. & Kartala, Xanthi-Isidora & Yannacopoulos, Athanasios N., 2013. "Stochastic Burgers PDEs with random coefficients and a generalization of the Cole–Hopf transformation," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3239-3272.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:8:p:3239-3272
    DOI: 10.1016/j.spa.2013.03.001
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    References listed on IDEAS

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    3. Yannacopoulos, Athanasios N., 2008. "Rational expectations models: An approach using forward-backward stochastic differential equations," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 251-276, February.
    4. Bonnet, Guillaume & Adler, Robert J., 2007. "The Burgers superprocess," Stochastic Processes and their Applications, Elsevier, vol. 117(2), pages 143-164, February.
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