Aug
29

## brownian bridge simulation

Similar to the spectral path construction method, the Brownian bridge is a way to construct a discretised Wiener process path by using the first Gaussian variates in a vector draw z to shape the overall features of the path, and then add more and more of the fine structure. The very first variate z1 is used to determine the realisation of theWiener path at the final time tn of our n-point discretisation of the path by setting Wtn = sqrt(tn)z1. The next variate is then used to determine the value of the Wiener process as it was realised at an intermediate timestep tj conditional on the realisation at tn (and at t0 = 0 which is, of course, zero). The procedure is then repeated to gradually fill in all of the realisations of the Wiener process at all intermediate points, in an ever refining algorithm.

here is a simulation of Brownian paths, brownian-bridge type simulation.

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OR maybe u can add more detailed comments on ur codes so that it can be more helpful? Thanks so much.