# name
Iterated logarithm law for anticipating stochastic differential equations

# metadata.dc.description.abstract[].value
We prove a functional law of iterated logarithm for the following kind of anticipating stochastic differential equations

$$
\xi_t^u=X_0^u+\frac{1}{\sqrt{\log \log u}} \sum_{j=1}^k \int_0^t A_j^u\left(\xi_s^u\right) \circ d W_s^j+\int_0^t A_0^u\left(\xi_s^u\right) d s
$$

where $u>e, W=\left\{\left(W_t^1, \ldots, W_t^k\right), 0 \leq t \leq 1\right\}$ is a standard $k$ dimensional Wiener process, $A_0^u, A_1^u, \ldots, A_k^u: \mathbb{R}^d \longrightarrow \mathbb{R}^d$ 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 .

# metadata.dc.relation.ispartof[].value
Journal of Theoretical Probability, 2007, vol. 21, num.3, p. 650-659

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Iterated logarithm law for anticipating stochastic differential equations