The telegraph process X(t), t > 0, (Goldstein, 1951) and the geometric telegraph process S(t) = s0 exp{(μ− 12σ)t+σX(t)} with μ a known constant and σ > 0 a parameter are supposed to be observed at n+1 equidistant time points ti = i∆n, i = 0, 1, . . . , n. For both models λ, the underlying rate of the Poisson process, is a parameter to be estimated. In the geometric case, also σ > 0 has to be es...

Self-stabilizing diffusions are stochastic processes, solutions of nonlinear stochastic differential equation, which are attracted by their own law. This specific self-interaction leads to singular phenomenons like non uniqueness of associated stationary measures when the diffusion leaves in some non convex environment (see [5]). The aim of this paper is to describe these invariant measures and...

We introduce Markovian cocycle perturbations of the groups of transformations associated with the classical and quantum stochastic processes with stationary increments, which are characterized by a localization of the perturbation to the algebra of events of the past. It is namely the definition one needs because the Markovian perturbations of the Kolmogorov flows associated with the classical ...

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...

This paper is a survey of results presented in the recent book Gyllenberg and Silvestrov [GS08]. This book is devoted to studies of quasi-stationary phenomena for nonlinearly perturbed stochastic processes and systems. New methods of asymptotic analysis for nonlinearly perturbed stochastic processes based on asymptotic expansions for perturbed renewal equation and recurrence algorithms for cons...

1. Stochastic Integration on Hilbert spaces 2 1.1. Gaussian measures on Hilbert spaces 2 1.2. Wiener processes on Hilbert spaces 6 1.3. Martingales on Banach spaces 7 1.4. Stochastic integration 8 1.5. Appendix: Stochastic integration w.r.t. cylindrical Wiener processes 12 2. Stochastic Di erential Equations on Hilbert spaces 13 2.1. Mild, weak and strong solutions 13 2.2. Existence and uniquen...

in this short review we look at recent advances in schramm-loewner evolution (sle) theory and its application to critical phenomena. the application of sle goes beyond critical systems to other time dependent, scale invariant phenomena such as turbulence, sand-piles and watersheds. through the use of sle, the evolution of conformally invariant paths on the complex plane can be followed; hence a...

the aim of this work is to understand the relation between time and place that an earthquake takes place. in order to answer this question, the modified level crossing (mlc) technique has been implemented. by studying two earthquakes, one in iran and one in california we came to the conclusion that there is a relation between time and place of an earthquake occurrence. as a matter of fact, this...

We review a coherent mesoscopic presentation of thermodynamics and fluctuations far from and near equilibrium, applicable to chemical reactions, energy transfer and transport processes, and electrochemical systems. Both uniform and spatially dependent systems are considered. The focus is on processes leading to and in non-equilibrium stationary states; on systems with multiple stationary states...

A method for the construction of approximate analytical expressions for the stationary marginal densities of general stochastic search processes is proposed. By the marginal densities, regions of the search space that with high probability contain the global optima can be readily defined. The density estimation procedure involves a controlled number of linear operations, with a computational co...