A stochastic differential equation specifies infinitesimal drift and random diffusion through a stochastic integral equation.
A weak solution may choose its probability space and driving Brownian motion as part of the solution. It is weaker than a strong solution, which must be adapted to a prescribed Brownian motion.
For a differential operator , the martingale problem asks for a process such thatis a local martingale for every test function in a suitable domain.
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A Stochastic Differential Equation (SDE) is a type of differential equation in which one or more of the terms are stochastic processes, meaning they involve random variables or noise. SDEs are used to model systems that are influenced by random effects or uncertainties, and they are widely applied in various fields, including finance, physics, biology, and engineering.