2013/02/18 by Maik Görgens, Maik Gorgens, Gorgens, Maik · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60G15 #60H10 #60J65 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60G15 #msc:60H10 #msc:60J65
paper · pdf · doi:10.48550/arxiv.1302.4186
22 pages, 1 figure
openalex publication_date 2013/02/18 · arxiv created 2014/12/04 · arxiv updated 2014/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize the notion of Gaussian bridges by conditioning Gaussian processes given that certain linear functionals of the sample paths vanish. We show the equivalence of the laws of the unconditioned and the conditioned process and by an application of Girsanov's theorem, we show that the conditioned process follows a stochastic differential equation (SDE) whenever the unconditioned process does. In the Markovian case, we are able to determine the coefficients in the SDE of the conditioned process explicitly. Our main example is Brownian motion on [0,1] pinned down in 0 at time 1 and conditioned to have vanishing area spanned by the sample paths.