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We show that the Langevin equation with fractional Brownian mo- tion noise also has a stationary solution and that the decay of its auto-covariance function is like that of a
Under some assumptions on the reward function C( · ) and the drift coefficient of the state process, we show that this game has a value.. Furthermore, this value function is
We do not pretend to remedy here to this extremely difficult problem, which ultimately should start from a Navier-Stokes type model and the analysis of its invariant measures.
In this section we prove the existence of a minimal stopping time which solves the Skorokhod embedding problem for random walk, and make some simple observations which show that
The expression just obtained for the distribution of coalescing Brownian motions is closely related to the formula for the transition density of the interlaced Brownian motions given
This article is organized as follows: In Section 2 we set the filtering problem with signal dependent observation noise and the framework for transforming this singular filtering
Keywords: Martingale, submartingale, distribution function, tail inequality, differential subordina- tion, conditional differential
In the case of a Markov chain over an infinite state space with a unique stationary distribution, the notion of a mixing time depends on the state of origination of the
