Definitions of mathematical integration | Stochastic calculus

Stratonovich integral

In stochastic processes, the Stratonovich integral (developed simultaneously by Ruslan Stratonovich and ) is a stochastic integral, the most common alternative to the Itô integral. Although the Itô integral is the usual choice in applied mathematics, the Stratonovich integral is frequently used in physics. In some circumstances, integrals in the Stratonovich definition are easier to manipulate. Unlike the Itô calculus, Stratonovich integrals are defined such that the chain rule of ordinary calculus holds. Perhaps the most common situation in which these are encountered is as the solution to Stratonovich stochastic differential equations (SDEs). These are equivalent to Itô SDEs and it is possible to convert between the two whenever one definition is more convenient. (Wikipedia).

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Related pages

Numerical integration | Wiener process | Quadratic variation | Chain rule | Stochastic process | Stochastic differential equation | Itô's lemma | Riemann sum | Langevin equation | Itô calculus | Euler–Maruyama method | Differentiable manifold | Adapted process | Partition of an interval | Limit (mathematics) | Riemann integral | Exterior algebra | Semimartingale | Riemann–Stieltjes integral | Stochastic calculus