Stochastic Diffusion with Oblique Reflection from an Evolving Set
dX =
(∇A2k)dt/A2k
+dBt
where
A2k(r,θ)
= kr2cos(2θ-π/k)sinπ/k
∝ r2cos(2θ-π/k)
on [0,∞)×[0,π/k].
Oblique reflection is perpendicular to the opposite boundary.
On exit:
1 hitmax hits
α = (δ+ε)/ξ = 2
Steps taken: 0
Behavior of the boundary (0,0) for SRBM for various α
For α ∈
(0,0) is
(-∞,0]
an entrance
(0,2)
regular, reflecting, & recurring
[2,∞)
exit, absorbing
Notes
Max hits is the number of times the diffusion will hit
[x,x+1)×[y,y+1) before stopping.
It can be as large as 9×1015
(but the diffusion will run for years if you do that).
It should be larger than 100, or
the diffusion will halt almost immediately.
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