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Fokker–Planck Equation
Fokker–Planck Equation
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Difficulty 6-6
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Intermediate
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Question 1 of 1
120s
intermediate (6/10)
state theorem
For the SDE
d
X
t
=
b
(
X
t
)
d
t
+
σ
(
X
t
)
d
W
t
, the Fokker-Planck equation describes the evolution of the density
p
(
x
,
t
)
. Which PDE is it?
Hide and think first
A.
∂
t
p
=
b
∂
x
p
+
2
1
σ
2
∂
xx
p
, the Kolmogorov *backward* equation applied to
p
B.
p
(
x
,
t
)
=
∫
K
(
x
,
y
,
t
)
p
0
(
y
)
d
y
, an integral equation with
K
the heat kernel of the SDE generator
C.
∂
t
p
=
−
∂
x
(
b
p
)
+
2
1
∂
xx
(
σ
2
p
)
, the Kolmogorov forward equation
D.
∂
t
p
=
∇
⋅
(
σ
2
∇
p
)
, a pure diffusion equation that ignores the drift contribution
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