Geodesic
General theorems for numerical approximation of stochastic processes on the Hilbert space $H_2([0,T], \mu,\bbfR^d)$
Electronic transactions on numerical analysis, Tome 16 (2003), pp. 50-69.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: General theorems for the numerical approximation on the separable Hilbert space IR !"$#\% \('0)213'546' 78 of cadlag, -adapted stochastic processes with -integrable second moments is presented for nonrandom intervals #@9BAC8 4 and positive measure . The use of the theorems is illustrated by the special case of systems of ordinary \% \('D)21 4 stochastic differential equations (SDEs) and their numerical approximation given by the drift-implicit Euler method under one-sided Lipschitz-type conditions.$
Classification : 65C20, 65C30, 65C50, 60H10, 37H10, 34F05
Keywords: stochastic-numerical approximation, stochastic Lax-theorem, ordinary stochastic differential equations, numerical methods, drift-implicit Euler methods, balanced implicit methods 
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     author = {Schurz, Henri},
     title = {General theorems for numerical approximation of stochastic processes on the {Hilbert} space $H_2([0,T], \mu,\bbfR^d)$},
     journal = {Electronic transactions on numerical analysis},
     pages = {50--69},
     publisher = {mathdoc},
     volume = {16},
     year = {2003},
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     url = {http://geodesic.mathdoc.fr/item/ETNA_2003__16__a7/}
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Schurz, Henri. General theorems for numerical approximation of stochastic processes on the Hilbert space $H_2([0,T], \mu,\bbfR^d)$. Electronic transactions on numerical analysis, Tome 16 (2003), pp. 50-69. http://geodesic.mathdoc.fr/item/ETNA_2003__16__a7/