Importance sampling, Fokker-Planck and Langevin equations

If we assume a discrete set of events, our initial probability distribution function can be given by

$$w_i(0) = \delta_{i,0},$$

and its time-development after a given time step $\Delta t=\epsilon$ is

$$w_i(t) = \sum_{j}W(j\rightarrow i)w_j(t=0).$$

The continuous analog to $w_i(0)$ is

$$w(\mathbf{x})\rightarrow \delta(\mathbf{x}),$$

where we now have generalized the one-dimensional position $x$ to a generic-dimensional vector $\mathbf{x}$. The Kroenecker $\delta$ function is replaced by the $\delta$ distribution function $\delta(\mathbf{x})$ at $t=0$.

• «
• 1
• ...
• 6
• 7
• 8
• 9
• 10
• 11
• 12
• 13
• 14
• 15
• 16
• 17
• 18
• 19
• 20
• 21
• 22
• 23
• ...
• 50
• »