Using stochastic differential equations we can successfully model systems that function in the presence of random perturbations. Such systems are among the basic objects of modern control theory. However, the very importance acquired by stochastic differential equations lies, to a large extent, in the strong connections they have with the equations of mathematical physics. It is well known that problems in mathematical physics involve ‘damned dimensions’, often leading to severe difficulties in solving boundary value problems. A way out is provided by stochastic equations, the solutions of which often come about as characteristics.
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