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Results tagged with ap.analysis-of-pdes
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user 220860
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
5
votes
0
answers
850
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Link between Fokker-Planck equation and Feynman-Kac formula
According to the Feynman-Kac formula, we know the solution of the partial differential equation:
$${\frac {\partial u}{\partial t}}(x,t)+\mu (x,t){\frac {\partial u}{\partial x}}(x,t)+{\tfrac {1}{2}}\ …
- 71
0
votes
0
answers
259
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Solving Fokker–Planck equation
Consider the Fokker–Planck equation:
$${\displaystyle {\frac {\partial }{\partial t}}p(x,t)=-{\frac {\partial }{\partial x}}\left[\mu (x,t)p(x,t)\right]+{\frac {\partial ^{2}}{\partial x^{2}}}\left[D( …
- 71
2
votes
0
answers
653
views
Proof of the link between the Fokker–Planck equation and SDE?
I know the link between the Fokker–Planck equation and SDE given by the Feynman-Kac theorem is as follow:
$$d X_{t}=\mu\left(X_{t}, t\right) d t+\sigma\left(X_{t}, t\right) d W_{t}$$
$$\frac{\partial} …
- 71