Constraint Ornstein-Uhlenbeck bridges

Abstract

In this paper, we study the Ornstein-Uhlenbeck bridge process (i.e. the Ornstein-Uhlenbeck process conditioned to start and end at fixed points) constraints to have a fixed area under its path. We present both anticipative (in this case, we need the knowledge of the future of the path) and non-anticipative versions of the stochastic process. We obtain the anticipative description thanks to the theory of generalized Gaussian bridges while the non-anticipative representation comes from the theory of stochastic control. For this last representation, a stochastic differential equation is derived which leads to an effective Langevin equation. Finally, we extend our theoretical findings to linear bridge processes.

20 pages, 5 figures

References in corpus (2)

• Periodic Airy process and equilibrium dynamics of edge fermions in a trap
• Area distribution and the average shape of a Lévy bridge

Cited by in corpus (17)

• The Airy distribution: experiment, large deviations and additional statistics
• Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator
• Stochastic interpolation of sparsely sampled time series via multi-point fractional Brownian bridges
• Sweetest taboo processes
• Conditioned diffusion processes with an absorbing boundary condition for finite or infinite horizon
• Strongly constrained stochastic processes: the multi-ends Brownian bridge
• Generating stochastic trajectories with global dynamical constraints
• Conditioning diffusion processes with killing rates
• Microcanonical conditioning of Markov processes on time-additive observables
• Noise and error analysis and optimization in particle-based kinetic plasma simulations
• Conditioning diffusion processes with respect to the local time at the origin
• A Jump Ornstein-Uhlenbeck Bridge Based on Energy-optimal Control and Its Self-exciting Extension
• Transport properties of diffusive particles conditioned to survive in trapping environments
• Joint distribution of two Local Times for diffusion processes with the application to the construction of various conditioned processes
• On unbiased simulations of stochastic bridges conditioned on extrema
• CIR bridge for modeling of fish migration on sub-hourly scale
• Conditioning two diffusion processes with respect to their first-encounter properties