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

被引：5

作者：

Englezos, Nikolaos ^{[1
]}

Frangos, Nikolaos E. ^{[2
]}

Kartala, Xanthi-Isidora ^{[2
]}

Yannacopoulos, Athanasios N. ^{[2
]}

机构：

[1] Univ Piraeus, Dept Banking & Financial Management, Piraeus 18534, Greece

[2] Athens Univ Econ & Business, Dept Stat, Athens 10434, Greece

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2013年 / 123卷 / 08期

关键词：

Stochastic Burgers equation; Random coefficients; Generalized Cole-Hopf transformation; Stochastic heat equation; Stochastic Feynman-Kac formulas; Controllability; Contingent claim pricing; DIFFERENTIAL-EQUATIONS; CONTROLLABILITY;

D O I：

10.1016/j.spa.2013.03.001

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：3239 / 3272

页数：34

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