Hello,
I have reasons to expect that the following code

G[xx_,dt_]:=Exp[-xx^2/(4*dt)]/Sqrt[4*π*dt];
Integrate[(G[x-ksi,dt-dtau]-G[x+ksi,dt-dtau])*Erf[ksi/Sqrt[4*dtau]], {dtau,0,dt},{ksi,0,∞},Assumptions->{dt>0}]

should produce the following result:

dt*Erf[x/Sqrt[4*dt]]

This can be checked numerically using NIntegrate, although not without some unclear error messages in NIntegrate. Unfortunately, Integrate fails to produce the expected formula. It also fails to produce results of integration along dtau or ksi separately. I would appreciate any suggestions how to handle this sort of problems.
Leslaw