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XXIV: 28, 407-441, LNM 1426 (1990)
ÉMERY, Michel
On two transfer principles in stochastic differential geometry (Stochastic differential geometry)
Second-order stochastic calculus gives two intrinsic methods to transform an ordinary differential equation into a stochastic one (see Meyer 1657, Schwartz 1655 or Emery Stochastic calculus in manifolds). The first one gives a Stratonovich SDE and needs coefficients regular enough; the second one gives an Ito equation and needs a connection on the manifold. Discretizing time and smoothly interpolating the driving semimartingale is known to give an approximation to the Stratonovich transfer; it is shown here that another discretized-time procedure converges to the Ito transfer. As an application, if the ODE makes geodesics to geodesics, then the Ito and Stratonovich SDE's are the same
Comment: An error is corrected in 2649. The term ``transfer principle'' was coined by Malliavin, Géométrie Différentielle Stochastique, Presses de l'Université de Montréal (1978); see also Bismut, Principes de Mécanique Aléatoire (1981) and 1505
Keywords: Stochastic differential equations, Semimartingales in manifolds, Transfer principle
Nature: Original
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