The current state of a system is commonly given by the solution of a deterministic differential, algebraic, or integral equation. For example, the functions giving the displacements of the points of a solid satisfy partial differential equations obtained from equilibrium conditions, kinematic constraints, and material constitutive laws. Generally, it is not possible to solve analytically the equations defining the system state. Numerical methods are needed for their solution. Most numerical methods are global that is, they determine the solution everywhere or at a large number of points in a system even if the solution is needed at a single point.
KeywordsBrownian Motion Local Solution Sample Path Transition Probability Matrix Deterministic System
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