Stochastic Differential Equations and Models of Random Processes
UNIVERSITY OF VIRGINIA Charlottesville United States
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Let us suppose that we are investigating a system whose state can be adequately specified by n real numbers x1, , xn. We shall suppose that by some acceptable scientific theory it is predicted that, in the absence of disturbances from outside the system, the xi develop in time in accordance with certain differential equations, xI gI0 t,x, I-1,...,n. If there are disturbances or noises,n1t,...nrt, the underlying theory of such systems will often permit us to conclude that xI gI0 t,x sigma sub p1 gIp t,x np t, I 1, ..., n, which gIp is the sensitivity of the ith coordinate to the pth noise.
- Statistics and Probability