A stochastic process evolves in time in a random way. Just as a differential equation governs motion that is deterministic, a stochastic differential equation governs motion that is random, or at least subject to some random influences.
Analytical tricks, asymptotic analyses and numerical methods that are used to understand dynamics governed by nonlinear differential equations, are being extended to stochastic dynamics.
Solving a stochastic differential equation is akin to solving an ordinary differential equation: exact analytical solutions are seldom available, but paths can be generated in a matter of seconds on a computer.
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Last updated 16/05/03