Consider a piecewise smooth expanding map of the interval possessing several invariant subintervals and the same number of ergodic absolutely continuous invariant probability measures (ACIMs). After this system is perturbed to make the subintervals lose their invariance in such a way that there is a unique ACIM, we show how to approximate the diffusion coefficient for an observable of bounded v...

We present a stochastic model for networks with arbitrary degree distributions and average clustering coefficient. Many descriptions of networks are based solely on their computed degree distribution and clustering coefficient. We propose a statistical model based on these characterizations. This model generalizes models based solely on the degree distribution and is within the curved exponenti...

Planning for supply water demands (drinkable and irrigation water demands) is a necessary problem. For this purpose, three subjects must be considered (optimization of water supply systems such as volume of reservoir dams, optimization of released water from reservoir and prediction of next droughts). For optimization of volume of reservoir dams, yield model is applied. Reliability of yield mod...

This contribution is devoted to risk-sensitive and risk-neutral optimality in Markov decision chains. Since the traditional optimality criteria (e.g. discounted or average rewards) cannot reflect the variability-risk features of the problem, and using the mean variance selection rules that stem from the classical work of Markowitz present some technical difficulties, we are interested in expect...

In this paper we consider Markov-modulated diffusion risk reserve processes. Using diffusion approximation we show the relation to classical Markov-modulated risk reserve processes. In particular we derive a representation for the adjustment coefficient and prove some comparison results. Among others we show that increasing the volatility of the diffusion increases the probability of ruin.

In this paper, we prove a Donker theorem for one-dimensional processes generated by an operator with measurable coefficients. We construct a random walk on any grid on the state space, using the transition probabilities of the approximated process, and the conditional average times it spends on each cell of the grid. Indeed we can compute these quantities by solving some suitable elliptic PDE p...

We introduce a simple model for the pricing of European style options when the underlying dividend process is given by a geometric Brownian motion with Markov-modulated coefficients. It turns out that the corresponding stock process is characterized by both stochastic coefficients and jumps. Transform methods are used to recover option prices. The model is calibrated to market data and the resu...

for all polynomials of degree at most n with real coefficients. There is a huge literature about Markov-type inequalities for constrained polynomials. In particular, several essentially sharp improvements are known for various classes of polynomials with restricted zeros. Here we just refer to [1], and the references therein. Let P n be the collection of all polynomials of degree at most n with...

In this paper, a lattice model for the diffusional transport of chromatin-binding particles in the interphase cell nucleus is proposed. Sliding effects are studied in dense networks of chromatin fibers created by three different methods: Randomly distributed, noninterconnected obstacles, a random walk chain model with an attractive step potential, and a self-avoiding random walk chain model wit...

This paper proposes a discrete-state stochastic volatility model with duration-dependent mixing. The latter is directed by a high-order Markov chain with a sparse transition matrix. Ž . As in the standard first-order Markov switching MS model, this structure can capture turning points and shifts in volatility, due for example, to policy changes or news events. Ž . However, the duration-dependen...