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CUBATURE ON WIENER SPACE: PATHWISE CONVERGENCE
"... simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast computation of European option prices in generic diffusion models. We give a random walk interpretation of cubature and similar (e.g. the N ..."
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simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast computation of European option prices in generic diffusion models. We give a random walk interpretation of cubature and similar (e.g. the Ninomiya– Victoir) weak approximation schemes. By using rough path analysis, we are able to establish weak convergence for general pathdependent option prices. 1.
CENTRAL LIMIT THEOREMS ON STRATIFIED LIE GROUPS
"... Lindeberg theorem is derived on stratied nilpotent Lie groups, that is a normal convergence theorem for a triangular system of probability measures in case of bounded (homogeneous) moments of second order. ..."
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Lindeberg theorem is derived on stratied nilpotent Lie groups, that is a normal convergence theorem for a triangular system of probability measures in case of bounded (homogeneous) moments of second order.
Lindeberg{Feller theorems on Lie groups
"... The author has proved in [4] several versions of Lindeberg{Feller type central limit theorems on the Heisenberg group, that is, necessary and sucient conditions for a triangular array (n`)`=1;:::;kn;n>1 of probability measures on the Heisenberg group to converge to a Gauss measure. Lindeberg typ ..."
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The author has proved in [4] several versions of Lindeberg{Feller type central limit theorems on the Heisenberg group, that is, necessary and sucient conditions for a triangular array (n`)`=1;:::;kn;n>1 of probability measures on the Heisenberg group to converge to a Gauss measure. Lindeberg type condition was used in the form
FUNCTIONAL CENTRAL LIMIT THEOREMS ON LIE GROUPS. A SURVEY
, 1998
"... The general solution of the functional central limit problems for triangular arrays of random variables with values in a Lie group is described. The role of processes of nite variation is claried. The special case of processes with independent increments having Markov generator is treated. Connectio ..."
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The general solution of the functional central limit problems for triangular arrays of random variables with values in a Lie group is described. The role of processes of nite variation is claried. The special case of processes with independent increments having Markov generator is treated. Connections with HilleYosida theory for two{parameter evolution families of operators and with the martingale problem are explained.