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Alan
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Joined: December 19th, 2001, 4:01 am
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Re: Hunting the Dirac Delta

January 21st, 2023, 3:42 pm

You need delta or actually its derivative?
I have now no issues with delta nor its derivative. BTW p is transition probability, p(t = 0) = delta.

the Q can I write FPE in verry nice compact form and what are the advantages

p_t = (A (B p_x))_x

it's just another PDE.

You should be able to always transform to: 
p_t = (A (B p_x))_x + V(x) p
for all 1D problems, as all [$]D = 1[$] diffusion problems involve self-adjoint operators in a weighted L^2 space.
(See footnote 3, Ch. 2 in my Vol II book).

Doesn't work in [$] D \ge 2[$], where the "generic" diffusion operator is non-self-adjoint.   
 
User avatar
Alan
Posts: 2741
Joined: December 19th, 2001, 4:01 am
Location: California
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Re: Hunting the Dirac Delta

January 21st, 2023, 4:34 pm

Probably can drop the V(x) term.