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4 papers · 2 filters
Effective Filtering on a Random Slow Manifold
Huijie Qiao, Yanjie Zhang, Jinqiao Duan
This work is about a slow-fast data assimilation system when only slow components are observable. First, we obtain its low dimensional reduction via an invariant slow manifold. Sec…
A note on parameter estimation for discretely sampled SPDEs
Igor Cialenco, Yicong Huang
We consider a parameter estimation problem for one dimensional stochastic heat equations, when data is sampled discretely in time or spatial component. We prove that, the real valu…
Stochastic Representations for Solutions to Parabolic Dirichlet Problems for Nonlocal Bellman Equations
Ruoting Gong, Chenchen Mou, Andrzej Swiech
We prove a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton-Jacobi-Bellman integro-partial differ…
Schauder estimates for stochastic transport-diffusion equations with Lévy processes
Jinlong Wei, Jinqiao Duan, Guangying Lv
We consider a transport-diffusion equation with Lévy noises and Hölder continuous coefficients. By using the heat kernel estimates, we derive the Schauder estimates for the mild so…