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arXiv · 1407.3421

Stochastic bridges of linear systems

Yongxin Chen·Tryphon Georgiou
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Abstract

We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed to have known states at the boundary. Thus, the movement of the particles can be modeled as an Ornstein-Uhlenbeck process conditioned on position and velocity measurements at the two end-points. It is shown that optimal stochastic control provides a stochastic differential equation (SDE) that generates such a bridge as a degenerate diffusion process. Generalizations to higher order linear diffusions are considered.

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Yongxin Chen, Tryphon Georgiou. 2014-07-12. Stochastic bridges of linear systems. https://arxiv.org/abs/1407.3421

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