Semi-Stable Stochastic Processes

Dilatively stable stochastic processes and aggregate similarity

Dilatively stable processes generalize the class of infinitely divisible self-similar processes. We reformulate and extend the definition of dilative stability introduced by Iglói (2008) using characteristic functions. We also generalize the concept of aggregate similarity introduced by Kaj (2005). It turns out that these two notions are essentially the same for infinitely divisible processes. ...

Evolutionarily stable strategies for stochastic processes.

The classical definition of evolutionary stability assumes that the fitness of each phenotype is fully determined by the composition of phenotypes in the population and by the strategies of each of these phenotypes. In natural populations, however, stochasticity often plays a crucial role in determining the fitness of an individual and a deterministic fitness function is probably rather rare. F...

Extremal stochastic integrals: a parallel between max–stable processes and α−stable processes

We construct extremal stochastic integrals ∫ e E f(u)Mα(du) of a deterministic function f(u) ≥ 0 with respect to a random α−Fréchet (α > 0) sup–measure. The measure Mα is sup–additive rather than additive and is defined over a general measure space (E, E , μ), where μ is a deterministic control measure. The extremal integral is constructed in a way similar to the usual α−stable integral, but wi...

On One-dimensional Stochastic Equations Driven by Symmetric Stable Processes

We study stochastic equations Xt = x0 + ∫ t 0 b(u,Xu−) dZu, where Z is an one-dimensional symmetric stable process of index α with 0 < α ≤ 2, b : [0,∞) × IR → IR is a measurable diffusion coefficient, and x0 ∈ IR is the initial value. We give sufficient conditions for the existence of weak solutions. Our main results generalize results of P. A. Zanzotto [18] who dealt with homogeneous diffusion...

The KTH Visit in Semi-Markov Processes