In the present paper the Wick version of analytic functions with respect to a one dimensional Brownian motion is shown to be closely related to the backward heat equation. This fact provides representation theorems for a certain class of random variables in terms of Wick powers. In addition, we obtain explicit formulas for the action of some second quantization operators arising in the applications.
Wick product and backward heat equation / LANCONELLI A. - In: MEDITERRANEAN JOURNAL OF MATHEMATICS. - ISSN 1660-5446. - STAMPA. - 2:4(2005), pp. 367-379. [10.1007/s00009-005-0051-9]
Wick product and backward heat equation
LANCONELLI A
2005
Abstract
In the present paper the Wick version of analytic functions with respect to a one dimensional Brownian motion is shown to be closely related to the backward heat equation. This fact provides representation theorems for a certain class of random variables in terms of Wick powers. In addition, we obtain explicit formulas for the action of some second quantization operators arising in the applications.File in questo prodotto:
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