Suppose that i have the following equations that represent the probabilistic lanchester model :
source : probabilistic lanchester model
$$ R'(t) =-f(R(t),B(t)) $$ $$ B'(t) =-g(R(t),B(t)) $$
$$ P ({(R ,B)→(R-1,B)})= f(R,B)\times\Delta \\ $$ $$ P ({(R ,B)→(R,B-1)})= g(R,B)\times\Delta \\ $$ $$ P ({(R ,B)→(R,B)})= 1-f(R,B)\times\Delta -g(R,B)\times\Delta $$
Where :
$$ \Delta : \text{is a very small time step.} $$ $$ \\ R(t) \text{ and } B(t) \text{ represent effectifs evolution of the two opposite teams during the battle.} $$
$$ (R ,B)→(R-1,B) $$ represents the event where the red team effectif decrease by 1 during battle. R and B are integers and at t=0 : $$ R(t)=R(0) \;and\;B(t)=B(0) $$
My question is as follow :
How this system could be modeled as a markov-chain ?
Thank you for help in advance !