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

Nikolaos Englezos; Nikolaos Frangos; Xanthi-Isidora Kartala; Athanasios Yannacopoulos

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arXiv · 1106.1976

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

Nikolaos Englezos·Nikolaos Frangos·Xanthi-Isidora Kartala·Athanasios Yannacopoulos

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Abstract

This paper studies forward and backward versions of random Burgers equation (RBE) with stochastic coefficients. Firstly, 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.

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BibTeX RIS

Nikolaos Englezos, Nikolaos Frangos, Xanthi-Isidora Kartala, Athanasios Yannacopoulos. 2013-03-06. Stochastic Burgers PDEs with random coefficients and a generalization of the Cole-Hopf transformation. https://arxiv.org/abs/1106.1976

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