A class of stochastic differential equations given by dx(t) = f(x(t))dt + g(x(t))dW(t), x(t 0) = x 0, t 0 ≤ t ≤ T < +∞, are investigated. Upon making some suitable assumptions, the existence and uniqueness of solution for the equations are obtained. Moreover, the existence and uniqueness of solution for stochastic Lorenz system, which is illustrated by example, are in good agreement with the theoretical analysis.
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机译：dx（t）= f（x（t））dt + g（x（t））dW（t），x（t 0）= x 0，t 0≤t≤ T <+∞，进行了研究。通过做出一些适当的假设，可以得到方程解的存在性和唯一性。此外，以实例说明的随机Lorenz系统解的存在性和唯一性与理论分析相吻合。
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