2024/12/29 by Nacira Agram, Bernt Øksendal, Agram, Nacira +5
Economics, Econometrics and Finance · Physics and Astronomy · #Stochastic processes and financial applications #Advanced Thermodynamics and Statistical Mechanics #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2412.20572
We investigate conditional McKean-Vlasov equations driven by time-space white noise, motivated by the propagation of chaos in an N-particle system with space-time Ornstein-Uhlenbeck dynamics. The framework builds on the stochastic calculus of time-space white noise, utilizing tools such as the two-parameter Ito formula, Malliavin calculus, and orthogonal decompositions to analyze convergence and stochastic properties. Existence and uniqueness of solutions for the associated stochastic partial differential equations (SPDEs) are rigorously established. Additionally, an integral stochastic Fokker-Planck equation is derived for the conditional law, employing Fourier transform methods and stochastic analysis in the plane. The framework is further applied to a partial observation control problem, showcasing its potential for analyzing stochastic systems with conditional dynamics.