Nonlinear self-stabilizing processes – II: Convergence to invariant probability
نویسندگان
چکیده
منابع مشابه
Self-stabilizing processes in multi-wells landscape in R - Convergence∗
Self-stabilizing processes are non-markovian diffusions. The own law of the process intervenes in the drift. When the non-interacting part of the drift corresponds to the gradient of a convex potential, it has been proved in some different ways that such processes converge when the time goes to infinity. However, in a previous paper, it has been proved that there is non-uniqueness of the statio...
متن کاملConvergence to the Equilibria for Self - Stabilizing Processes in Double - Well Landscape
We investigate the convergence of McKean-Vlasov diffusions in a non-convex landscape. These processes are linked to nonlinear partial differential equation. According to our previous results, there are at least three stationary measures under simple assumptions. Hence, the convergence problem is not classical like in the convex case. By using the method in [Benedetto, Caglioti, Carrillo, Pulvir...
متن کاملConvergence of Invariant Measures of Truncation Approximations to Markov Processes
Let Q be the Q-matrixof an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augmentations of Q converge in total variation to the stationary distribution of the process. Twoconditions guaranteeing such convergence include exponential ergodicity and stochastic monoton...
متن کاملSelf-stabilizing processes in multi-wells landscape in R - Invariant probabilities∗
The aim of this work is to analyse the stationary measures for a particular class of non-markovian diffusions: the self-stabilizing processes. All the trajectories of such a process attract each other. This permits to exhibit a non-uniqueness of the stationary measures in the one-dimensional case, see [HT10a]. In this paper, the extension to general multi-wells lansdcape in general dimension is...
متن کاملSelf-stabilizing processes: uniqueness problem for stationary measures and convergence rate in the small noise limit
In the context of self-stabilizing processes, that is processes attracted by their own law, living in a potential landscape, we investigate different properties of the invariant measures. The interaction between the process and its law leads to nonlinear stochastic differential equations. In [7], the authors proved that, for linear interaction and under suitable conditions, there exists a uniqu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1998
ISSN: 0304-4149
DOI: 10.1016/s0304-4149(98)00019-2