The exit time and the exit location of a non-markovian diffusion is analyzed. More particularly, we focus on the so-called self-stabilizing process. The question has been studied by Herrmann, Imkeller and Peithmann in [HIP08]. Some results similar to the ones of Freidlin and Wentzell for classical diffusions have been proved. We aim to provide the same results by a method more intuitive. Our ar...

We examine the task of constructing self-stabilizing real-time decision systems, which take their input from an external environment, and present a series of results concerning compilers which force the property of self-stabilization onto such systems. We consider compilers that do and do not preserve termination applied to nite state and innnite state programs.

Dynamics in a distributed system are self-stabilizing if they are guaranteed to reach a stable state regardless of how the system is initialized. Game dynamics are uncoupled if each player’s behavior is independent of the other players’ preferences. For uncoupled players, recognizing an equilibrium is a distributed computational task. Self-stabilizing uncoupled dynamics, then, capture both resi...

the present work is aimed to find a new and efficient type of antioxidants for polypropylene. hence, effects of 3,3-bis(4-hydroxy-2-methyl-5-propan-2-ylphenyl)-2-benzofuran-1-one, generally known as thymolphthalein, on thermo-oxidative stability of polypropylene in solid and melt states were evaluated and compared with those of songnox 1010, an efficient commercially used antioxidant for the po...

A self-stabilizing system is one which can recover from transient faults in a nite number of steps. We present a theory for determining if a behavior speciication can be satissed with a self-stabilizing system and if not, then what the largest self-stabilizing subset and smallest self-stabilizing superset of the speciication is. The eeects of self-stabilizing behavior on the control of discrete...

A probabilistic self-stabilizing algorithm for a ring of identical processes is presented; the number of processes in the ring is odd, the processes operate synchronously, and communication is unidirectional in the ring. The normal function of the algorithm is to circulate a single token in the ring. If the initial state of the ring is abnormal, i.e. the number of tokens diiers from one, then e...

In this announcement, we report recent results where we address the open problem of snap-stabilization in messagepassing systems. (A full version of this paper is available as [3] at http://arxiv.org/abs/0802.1123.)