Analysis of SPDEs Arising in Path Sampling Part I: The Gaussian Case

Details Analysis of SPDEs Arising in Path Sampling Part I: The Gaussian Case Analysis of SPDEs Arising in Path Sampling Part I: The Gaussian Case

2006-01-05

arxiv.org/abs/math/0601095v1

Communications in Mathematical Sciences, vol. 3, no. 4, pp. 587-603, 2005

Mathematics

Probability

Scientific paper

In many applications it is important to be able to sample paths of SDEs conditional on observations of various kinds. This paper studies SPDEs which solve such sampling problems. The SPDE may be viewed as an infinite dimensional analogue of the Langevin SDE used in finite dimensional sampling. Here the theory is developed for conditioned Gaussian processes for which the resulting SPDE is linear. Applications include the Kalman-Bucy filter/smoother. A companion paper studies the nonlinear case, building on the linear analysis provided here.

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