Feynman-Kac formula in action.
$begingroup$
Briefly speaking, the Feynman-Kac formula gives a way for constructing $C^2$ functions satisfying certain PDEs in the classical sense (at least, it's how it is explained in Oksendal's book that I am currently reading).
This method relies on Ito-diffusions and can be easily implemented from a numerical viewpoint, offering a PDE Monte-Carlo solver.
Again, let me point out how the theory relies on a classical-derivative viewpoint.
My question is: can this technique be extended to more general Sobolev spaces, in order to construct Monte Carlo methods for certain PDEs in a weak sense?
A good reference would suffice.
Thanks in advance for the help.
pde numerical-methods stochastic-calculus monte-carlo
asked Dec 18 '18 at 12:09
user233650user233650
48629
$endgroup$
add a comment |
$begingroup$
Briefly speaking, the Feynman-Kac formula gives a way for constructing $C^2$ functions satisfying certain PDEs in the classical sense (at least, it's how it is explained in Oksendal's book that I am currently reading).
This method relies on Ito-diffusions and can be easily implemented from a numerical viewpoint, offering a PDE Monte-Carlo solver.
Again, let me point out how the theory relies on a classical-derivative viewpoint.
My question is: can this technique be extended to more general Sobolev spaces, in order to construct Monte Carlo methods for certain PDEs in a weak sense?
A good reference would suffice.
Thanks in advance for the help.
pde numerical-methods stochastic-calculus monte-carlo
asked Dec 18 '18 at 12:09
user233650user233650
48629
$endgroup$
add a comment |
$begingroup$
Briefly speaking, the Feynman-Kac formula gives a way for constructing $C^2$ functions satisfying certain PDEs in the classical sense (at least, it's how it is explained in Oksendal's book that I am currently reading).
This method relies on Ito-diffusions and can be easily implemented from a numerical viewpoint, offering a PDE Monte-Carlo solver.
Again, let me point out how the theory relies on a classical-derivative viewpoint.
My question is: can this technique be extended to more general Sobolev spaces, in order to construct Monte Carlo methods for certain PDEs in a weak sense?
A good reference would suffice.
Thanks in advance for the help.
pde numerical-methods stochastic-calculus monte-carlo
asked Dec 18 '18 at 12:09
user233650user233650
48629
$endgroup$
Briefly speaking, the Feynman-Kac formula gives a way for constructing $C^2$ functions satisfying certain PDEs in the classical sense (at least, it's how it is explained in Oksendal's book that I am currently reading).
This method relies on Ito-diffusions and can be easily implemented from a numerical viewpoint, offering a PDE Monte-Carlo solver.
Again, let me point out how the theory relies on a classical-derivative viewpoint.
My question is: can this technique be extended to more general Sobolev spaces, in order to construct Monte Carlo methods for certain PDEs in a weak sense?
A good reference would suffice.
Thanks in advance for the help.
pde numerical-methods stochastic-calculus monte-carlo
pde numerical-methods stochastic-calculus monte-carlo
asked Dec 18 '18 at 12:09
user233650user233650
48629
asked Dec 18 '18 at 12:09
user233650user233650
48629
edited Dec 18 '18 at 16:32
user233650
asked Dec 18 '18 at 12:09
user233650user233650
48629
asked Dec 18 '18 at 12:09
user233650user233650
48629
asked Dec 18 '18 at 12:09
user233650user233650
48629
48629
add a comment |
add a comment |
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