Year: 2022
Type: article
Abstract: When the unconditioned process is a diffusion submitted to a space-dependent killing rate k ( x → ) , various conditioning constraints can be imposed for a finite time horizon T . We first analyze the conditioned process when one imposes both the surviving distribution at time T and the killing-distribution for the intermediate times t ∈ [0, T ]. When the conditioning constraints are less-detailed than these full distributions, we construct the appropriate conditioned processes via the optimization of the dynamical large deviations at level 2.5 in the presence of the conditioning constraints that one wishes to impose. Finally, we describe various conditioned processes for the infinite horizon T → +∞. This general construction is then applied to two illustrative examples in order to generate stochastic trajectories satisfying various types of conditioning constraints: the first example concerns the pure diffusion in dimension d with the quadratic killing rate k ( x → ) = γ x → 2 , while the second example is the Brownian motion with uniform drift submitted to the delta killing rate k ( x ) = kδ ( x ) localized at the origin x = 0.
Authors: Alain Mazzolo, Cécile Monthus
Institutions: Commissariat à l'Énergie Atomique et aux Énergies Alternatives, Université Paris-Saclay, CEA Paris-Saclay - Etablissement de Saclay, CEA Paris-Saclay, Service d'Étude des Réacteurs et de Mathématiques Appliquées, Centre National de la Recherche Scientifique, Institut de Physique Théorique
Language: Latvian
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4223600759