**G. BUFFONI** and **E. CUPINI**

*The adjoint advection-diffusion equation in stationary and time dependent
problems: a reciprocity relation*

**Abstract**:
Both stationary and time dependent adjoint problems associated to
advection-diffusion problems are formulated.
The adjoint problem is then interpreted as a model for an advection-diffusion
process of a tracer called the "adjoint tracer". The construction of such a
model is a sine qua non condition for the integration of the adjoint
advection-diffusion equation by means of probabilistic methods.
A reciprocity relation relating direct and adjoint transition probability
density functions is derived. Strategies to solving advection-diffusion
problems by means of Monte Carlo methods are illustrated.

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