# Construct recurrence relation for the temporal evolution of a Master equation

+ 1 like - 0 dislike
132 views

Say that we have a system evolving over discrete timesteps.

The quantity we are interested is X and is given by a distribution $P_X$. This distribution is evolving temporally, and we have a nonlinear equation $F$ that gives us this evolution.

$P_{\Delta X}(x;n) = F\big(~P_X(x;n)~,~P_X(x;n-1)~\big)~~~,~~~n \in \mathbb{N}$

where: $~~~X(x;n+1)=X(x;n)+\Delta X(x;n)$

We also know the initial condition $P_X(x;0) = \delta(x-k)$.

Unfortunately $X$ and $\Delta X$ are correlated.

My question is, what is the appropriate framework to investigate the evolution of $P_X$?

This post imported from StackExchange Physics at 2016-05-21 10:16 (UTC), posted by SE-user Dionysios Gerogiadis

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsOv$\varnothing$rflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.