Stochastic Gronwall inequality

Stochastic Gronwall inequality is a generalization of Gronwall's inequality and has been used for proving the well-posedness of path-dependent stochastic differential equations with local monotonicity and coercivity assumption with respect to supremum norm. == Statement == Let X ( t ) , t ≥ 0 {\displaystyle X(t),\,t\geq 0} be a non-negative right-continuous ( F t ) t ≥ 0 {\displaystyle ({\mathcal {F}}_{t})_{t\geq 0}} -adapted process.

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Stochastic Gronwall inequality

Stochastic Gronwall inequality is a generalization of Gronwall's inequality and has been used for proving the well-posedness of path-dependent stochastic differential equations with local monotonicity and coercivity assumption with respect to supremum norm. == Statement == Let X ( t ) , t ≥ 0 {\displaystyle X(t),\,t\geq 0} be a non-negative right-continuous ( F t ) t ≥ 0 {\displaystyle ({\mathcal {F}}_{t})_{t\geq 0}} -adapted process.

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Source: Wikipedia "Stochastic Gronwall inequality" · CC BY-SA 4.0

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