A Method of Generalized Characteristics
Jan 1982 · American Mathematical Society: Memoirs of the American Mathematical Society Ibhuku elingu-266 · American Mathematical Soc.
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The classical and Brownian methods of characteristics are generalized to analyze evolution equations of arbitrary order. Calculi of higher orders, analogous to first order classical calculus and second order Ito calculus, are constructed. Solutions of differential equations in the calculi become characteristic propagators of higher order partial differential equations. The solutions of these partial differential equations are then represented as averages of random samples of initial data based on these characteristic flows, in a general sense.
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