Feynman-Kac theorem about Cauchy problem of extended second-order parabolic equation (Q2704967)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Feynman-Kac theorem about Cauchy problem of extended second-order parabolic equation |
scientific article |
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19 June 2001
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stochastic differential equation
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extended second-order linear parabolic equation
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Poisson process
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Cauchy problem
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Feyman-Kac theorem
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Feynman-Kac theorem about Cauchy problem of extended second-order parabolic equation (English)
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Motivated by applications in financial mathematics, the solutions to stochastic differential equations with jump diffusion are briefly discussed. An explicit solution to backward heat equation is studied. The authors consider also a stochastic differential equation driving by a \(d\)-dimensional Brownian motion and a \(d\)-dimensional Poisson process. They investigate under which conditions the solution of Cauchy problem is unique. Furthermore, using Feynman-Kac formula associated to the extended second-order linear parabolic equation the solution can be explicitly represented.
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