One-Dimensional Stratonovich Differential Equations
Martin, Jaime San
Ann. Probab., Tome 21 (1993) no. 4, p. 509-553 / Harvested from Project Euclid
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We consider one-dimensional stochastic differential equations of the Stratonovich type: $dX_t = \sum_i\sigma_i(t, w, X_t)\circ dZ^i_t + \sum_k h_k(t, w, X_t)dA^k_t,$ where $Z^i$ are continuous semimartingales, and $A^k$ are continuous finite variation processes. We extend the definition of the Fisk-Stratonovich integral for a large class of coefficients $\sigma_i$, and under suitable conditions we prove existence and uniqueness for that equation.
Publié le : 1993-01-14
Classification:  Stratonovich differential equations,  semimartingales,  strong solutions,  60H10,  60H05 
@article{1176989414,
     author = {Martin, Jaime San},
     title = {One-Dimensional Stratonovich Differential Equations},
     journal = {Ann. Probab.},
     volume = {21},
     number = {4},
     year = {1993},
     pages = { 509-553},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176989414}
}

Martin, Jaime San. One-Dimensional Stratonovich Differential Equations. Ann. Probab., Tome 21 (1993) no. 4, pp.  509-553. http://gdmltest.u-ga.fr/item/1176989414/