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Demonstrates stabilization by noise in linear stochastic differential equations, indicating important insights for mathematical models.
The well-known effect of stabilization by noise for Ito’s scalar linear stochastic differential equation was proven by R.Z. Khasminskii more than 50 years ago. Here, a similar statement is obtained for a system of linear stochastic differential equations. The obtained result is illustrated on the system of two linear stochastic differential equations via several special examples with numerical simulations and figures.
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Leonid Shaikhet (2026) studied this question.
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