We consider a stochastic process (Xt)t≥0 that grows linearly in time and experiences collapses at times governed by a Poisson process with rate λ. The collapses are modeled by multiplying the process level by a random variable supported on [0, 1). For the hitting time defined as τy = inf{t > 0|Xt = y} we derive power series for the Laplace transform and all moments. We further discuss the asymp...

Many real phenomena may be modelled as locally finite unions of d-dimensional time dependent random closed sets in R, described by birth-and-growth stochastic processes, so that their mean volume and surface densities, as well as the so called mean extended volume and surface densities, may be studied in terms of relevant quantities characterizing the process. We extend here known results in th...

We propose a variety of models of random walk, discrete in space and time, suitable for simulating stable random variables of arbitrary index α (0 < α ≤ 2), in the symmetric case. We show that by properly scaled transition to vanishing space and time steps our random walk models converge to the corresponding continuous Markovian stochastic processes, that we refer to as Lévy-Feller diffusion pr...

mathematical modeling of supply chain operations has proven to be one of the most complex tasks in the field of operations management and operations research. despite the abundance of several modeling proposals in the literature; for vast majority of them, no effective universal application is conceived. this issue renders the proposed mathematical models inapplicable due largely to the fact th...

We shall deal only with processes which evolve at discrete instances of time. Typically, the time index can be k0, k0 + 1, . . . , N , with k0 and N both finite, or it can be the nonnegative integers Z+ = 0, 1, . . ., or it can be all the integers Z. Let T be such an index set, which can be finite or countably infinite. Assume also that there is an underlying probability space (Ω,S, P ) with re...

Many applications require stochastic processes specified on twoor higherdimensional domains; spatial or spatial-temporal modelling, for example. In these applications it is attractive, for conceptual simplicity and computational tractability, to propose a covariance function that is separable; e.g. the product of a covariance function in space and one in time. This paper presents a representati...

I introduce and study dynamic persuasion mechanisms. A principal privately observes the evolution of a stochastic process and sends messages over time to an agent. The agent takes actions in each period based on her beliefs about the state of the process and the principal wishes to influence the agent’s action. I characterize the optimal persuasion mechanism and apply it to some examples.

The underlying assumption for using seasonal dummies in a regression is that the seasonality of the dependent variable is deterministic. Many economic variables show a regular seasonal pattern, with peaks occuring in the same season year after year. Such a regular seasonal pattern can also be a result of an integrated stochastic process. This paper examines some consequences of deterministic mo...

We consider a model for systems perturbed by dichotomous noise, in which the hazard rate function of a random lifetime is subject to additive time-alternating perturbations described by the telegraph process. This leads us to define a real-valued continuous-time stochastic process of alternating type expressed in terms of the integrated telegraph process for which we obtain the probability dist...

An integrated fuzzy-stochastic risk assessment (IFSRA) approach was developed in this study to systematically quantify both probabilistic and fuzzy uncertainties associated with site conditions, environmental guidelines, and health impact criteria. The contaminant concentrations in groundwater predicted from a numerical model were associated with probabilistic uncertainties due to the randomnes...