We introduce a multidimensional walk with memory and random tendency. The asymptotic behaviour is characterized, proving a law of large numbers and showing a phase transition from diffusive to superdiffusive regimes. In first case, we obtain a functional limit theorem to Gaussian vectors. In superdiffusive, we obtain strong convergence to a non-Gaussian random vector and characterize its moments.

中文翻译：

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具有随机趋势的多维游走

我们引入了具有记忆和随机趋势的多维行走。渐近行为被表征，证明了大数定律并显示了从扩散到超扩散机制的相变。在第一种情况下，我们获得了高斯向量的泛函极限定理。在超扩散中，我们获得了对非高斯随机向量的强收敛性并表征了它的矩。