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INICIO | 13 de mayo de 2021

Differential equations driven by rough signals.

Título inglés Differential equations driven by rough signals.
Título español Ecuaciones diferenciales dirigidas por señales con trayectorias accidentadas.
Autor/es Lyons, Terry J.
Organización Dep. Math. Imp. Coll. London, Londres, Reino Unido
Revista 0213-2230
Publicación 1998, 14 (2): 215-310, 32 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés This paper aims to provide a systematic approach to the treatment of differential equations of the type
dyt = Σi fi(yt) dxti
where the driving signal xt is a rough path. Such equations are very common and occur particularly frequently in probability where the driving signal might be a vector valued Brownian motion, semi-martingale or similar process.
However, our approach is deterministic, is totally independent of probability and permits much rougher paths than the Brownian paths usually discussed. The results here are strong enough to treat the main probabilistic examples and significantly widen the class of stochastic processes which can be used to drive stochastic differential equations. (For a simple example see [10], [1]).
We hope our results will have an influence on infinite dimensional analysis on path spaces, loop groups, etc. as well as in more applied situations. Variable step size algorithms for the numerical integration of stochastic differential equations [8] have been constructed as a consequence of these results.
Clasificación UNESCO 120808
Palabras clave español Ecuaciones diferenciales estocásticas ; Proceso de difusión ; Movimiento browniano
Código MathReviews MR1654527
Código Z-Math Zbl 0923.34056
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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)