Tag Archives: heat equation

Random Walk and Differential Equations (II)

Posted on October 13, 2012 by limsup

1-Dimensional Heat Equation Consider the case of 1-dimensional random walk. The equation (*) from the previous post gives: for t≥0. Suppose the intervals between successive time/space points are variable. Let’s rewrite it in the following form: Setting δt ≈ ε2 and δx ≈ ε, we divide both … Continue reading →

Posted in Notes | Tagged , , , , , , | Leave a comment

Random Walk and Differential Equations (I)

Posted on October 12, 2012 by limsup

Consider discrete points on the real line, indexed by the integers … -3, -2, -1, 0, 1, 2, … . A drunken man starts at position 0 and time 0. At each time step, he may move to the left … Continue reading →

Posted in Notes | Tagged , , , | Leave a comment