u=Manipulate[

Plot3D[f[x,t,β,d],{x,minX,maxX},{t,.01,simTime},
PlotRange->{Automatic,{0,maxTime},{0,maxF}},
AxesLabel->{"x","t","f(x,t)"},
PlotLabel->Style["Solution to \!\(\*FractionBox[\(\(∂f\)\(\\ \)\), \(∂t\)]\) = -β\!\(\*FractionBox[\(\(∂f\)\(\\ \)\), \(∂x\)]\)+ D\!\(\*FractionBox[\(\*SuperscriptBox[\(∂\), \(2\)]\\ f\), \(∂\*SuperscriptBox[\(x\), \(2\)]\)]\) \nEinstein-Wiener process",Small],
ImagePadding->55,ImageSize->500,
PlotPoints->ControlActive[{50,Round[simTime/10]+5},{50,Round[simTime/10]+5}],
Mesh->ControlActive[10,10],MaxRecursion->0]
,
{{β,.4,"β (Drift)="},-1,1,.01,AppearanceElements->All,ContinuousAction->False},
{{d,5,"D (Diffusion)="},.1,5,.01,AppearanceElements->All,ContinuousAction->True},
{{simTime,maxTime,"simulation time="},.1,maxTime,.1,AppearanceElements->All,SynchronousUpdating->True},
Delimiter,
{{maxF,.1,"max F="},.01,3,.01,AppearanceElements->All,ContinuousAction->True},
AutorunSequencing->{{3,80}},
Initialization:>
{
minX=-300; maxX=300; maxTime=1000;

f[x_,t_,β_,Diffusion_]:=Module[{μ,σ},
μ=β t;
σ=(Sqrt[2 Diffusion t]);
(1/(σ(Sqrt[2π])))Exp[-(1/2)(((x-μ)/σ))^2]
]
}
]