A probabilistic representation for the solution of the partial differential equation $\frac{\partial}{\partial t}u(t,x)=-\alpha \Delta^2 u(t,x) -V(x)u(t,x)$, $\alpha\in\C_+$, is constructed in terms of the expectation with respect to the measure associated to a complex-valued stochastic process.
Probabilistic representations for the solution of higher order differential equations
Mazzucchi, Sonia
2013-01-01
Abstract
A probabilistic representation for the solution of the partial differential equation $\frac{\partial}{\partial t}u(t,x)=-\alpha \Delta^2 u(t,x) -V(x)u(t,x)$, $\alpha\in\C_+$, is constructed in terms of the expectation with respect to the measure associated to a complex-valued stochastic process.File in questo prodotto:
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