Stochastic Feynman-Kac formula
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The stochastic partial differential equation called stochastic Feynman- Kac formula is investigated. For any distribution \(g\in {\mathcal D}'(R^ d)\) the author proves that the equation has a unique solution g exp- \(\int^{t}_{0}V(\cdot +w_ s)ds\) defining a semimartingale with the strong Markov property with continuous trajectories in \({\mathcal D}'(R^ d)\), and the infinitesimal generator of the semigroup is explicitly evaluated. Similar methods are applied to the Schrödinger equation.
Stochastic partial differential equations (aspects of stochastic analysis), stochastic Feynman-Kac formula, Schrödinger equation, Martingales with continuous parameter, PDEs with randomness, stochastic partial differential equations, semimartingale with the strong Markov property
Stochastic partial differential equations (aspects of stochastic analysis), stochastic Feynman-Kac formula, Schrödinger equation, Martingales with continuous parameter, PDEs with randomness, stochastic partial differential equations, semimartingale with the strong Markov property
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