Iterated logarithm law for anticipating stochastic differential equations

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dc.creatorMarquez-Carreras, D.
dc.creatorRovira, C.
dc.date2007-07-18
dc.date.accessioned2026-07-07T08:18:58Z
dc.date.available2026-07-07T08:18:58Z
dc.descriptionWe prove a functional law of iterated logarithm for the following kind of anticipating stochastic differential equations $$ξ^u_t=X_0^u+\frac{1}{\sqrt{\log\log u}}\sum_{j=1}^k \int_0^{t} A_j^u(ξ^u_s)\circ dW_{s}^j+ \int_0^{t} A_0^u(ξ^u_s)ds,$$ where $u>e$, $W=\{(W_t^1,...,W_t^k), 0\le t\le 1\}$ is a standard $k$-dimensional Wiener process, $A_0^u,A_1^u,..., A_k^u:\mathbb{R}^d\longrightarrow \mathbb{R}^d$ are functions of class $\mathcal{C}^2$ with bounded partial derivatives up to order 2, $X_0^u$ is a random vector not necessarily adapted and the first integral is a generalized Stratonovich integral .
dc.identifierhttps://arxiv.org/abs/0707.2650
dc.identifierhttp://arxiv.org/abs/0707.2650
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134619
dc.subjectProbability
dc.subject60H10, 60H15
dc.titleIterated logarithm law for anticipating stochastic differential equations
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