Talk:Reflected Brownian motion

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Simulation[edit]

Is anyone aware of any freely available code for RBM simulation in multiple dimensions? I'm aware of QNET for stationary simulation, however this code is twenty years old and doesn't readily compile on a modern machine. (A colleague has managed to get the 16-bit windows code running using DOSBox.) I have not yet found any code for transient simulation. Gareth Jones (talk) 14:11, 5 December 2012 (UTC)[reply]

Error?[edit]

There seem to be sign errors in the formulas for transient and stationary distribution. For example, if the Brownian motion is dz=mu*dt+sigma*dW, mu<0, then it seems as if the stationary distribution should be 1-Exp[2*mu/sigma^2*z] (without the minus sign in front of mu in the exponent). — Preceding unsigned comment added by 216.165.95.68 (talk) 21:21, 10 December 2014 (UTC)[reply]

Non-orthant boundaries and directions of reflection[edit]

The current definition seems to assume that the boundaries correspond to orthant boundaries (Z_j = 0). The case studied by Harrison and Williams (reference [8] at the moment) allows more general constraints, such as general polyhedron. Could someone who understands this better than I do please update the definition to allow more general reflecting boundaries, or explain how the current definition captures that case?

I came here looking for the intuition behind the direction of reflection. It would be nice to have some description of that too. In particular, a particle with Brownian motion doesn't have momentum, and so I assume the "push" lasts only as long as there is contact. It would be useful to relate that to the local time, and discuss how the local time at a boundary behaves (conditions for it to be non-zero, intuition of why it is non-zero, how quickly it grows with time in a simple case such as drift towards a single reflecting boundary in 2-D etc.). LachlanA (talk) 01:18, 16 October 2023 (UTC)[reply]

What would immensely improve this article[edit]

Two things that would immensely improve this article are 1) first presenting just one maximally simple example of reflected brownian motion before defining the most general form of it, and 2) including an illustration that depicts such a simple example.