Alexander Roitershtein

One-dimensional linear recursions with Markov-dependent coefficients

For a class of stationary Markov-dependent sequences

A note on multitype branching processes with immigration in a random environment.

(A_n,B_n)\in\mathbb{R}^2,

On a directionally reinforced random walk

we consider the random linear recursion

On probabilistic analog automata

S_n=A_n+B_nS_{n-1},

On the range of the transient frog model on ℤ

n\in\mathbb{Z},

Divergent Perpetuities Modulated by Regime Switches

and show that the distribution tail of its stationary solution has a power law decay.

Stochastic analysis of the motion of DNA nanomechanical bipeds

We consider a multitype branching process with immigration in a random environment introduced by Key in [Ann. Probab. 15 (1987) 344-353]. It was shown by Key that, under the assumptions made in [Ann. Probab. 15 (1987) 344-353], the branching process is subcritical in the sense that it converges to a proper limit law. We complement this result by a strong law of large numbers and a central limit theorem for the partial sums of the process. In addition, we study the asymptotic behavior of oscillations of the branching process, that is, of the random segments between successive times when the extinction occurs and the process starts again with the next wave of the immigration.

On Wallis-type Products and Pólya's Urn Schemes

We consider a generalized version of a directionally reinforced random walk, which was originally introduced by Mauldin, Monticino, and von Weizsacker in [20]. Our main result is a stable limit theorem for the position of the random walk in higher dimensions. This extends a result of Horvath and Shao [13] that was previously obtained in dimension one only (however, in a more stringent functional form).

Optimal control of a stochastic processing system driven by a fractional Brownian motion input

We consider probabilistic automata on a general state space and study their computational power. The model is based on the concept of language recognition by probabilistic automata due to Rabin (Inform. Control 3 (1963) 230) and models of analog computation in a noisy environment suggested by Maass and Orponen (Neural Comput. 10 (1998) 1071), and Maass and Sontag (Neural Comput. 11 (1999) 771). Our main result is a generalization of Rabins reduction theorem that implies that under very mild conditions, the computational power of such automata is limited to regular languages.