A stochastic Lagrangian particle model and nonlinear filtering for three dimensional Euler flow with jumps

Sritharan, S. S.; Xu, Meng

doi:10.31390/cosa.5.3.07

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2013

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“…This subject was initiated in [38][39][40][41][42] and in [15] a reacting and diffusing system was studied. In this work, we derive the FujisakiKallianpur-Kunita (FKK) equation and the Zakai equation for the nonlinear filtering of stochastic Navier-Stokes equation with Itô-Lévy noise, and prove existence and uniqueness of the measure-valued solution in certain class of measures.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Filtering of Stochastic Navier-Stokes Equation with Itô-Lévy Noise

Fernando

Sritharan

2013

Stochastic Analysis and Applications

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In this article, we study the existence and uniqueness of the strong pathwise solution of stochastic Navier-Stokes equation with Itô-Lévy noise. Nonlinear filtering problem is formulated for the recursive estimation of conditional expectation of the flow field given back measurements of sensor output data. The corresponding Fujisaki-Kallianpur-Kunita and Zakai equations describing the time evolution of the nonlinear filter are derived. Existence and uniqueness of measure-valued solutions are proven for these filtering equations.

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Section: Introductionmentioning

confidence: 99%