In this article we study multivariate continuous-time autoregressive moving-average (MCARMA) processes with values in convex cones. More specifically, introduce matrix-valued MCARMA L\'evy noise and present necessary sufficient conditions for from class to be cone valued. We derive specific hands-on the following two cases: First, classical on $\mathbb{R}_{d}$ positive orthant $\mathbb{R}_{d}^{...

We introduce a variable step size method for the numerical approximation of path-wise solutions to stochastic diierential equations (SDE's). The method, which is dependent on a representation of Brownian paths as binary trees, involves estimation of local errors and of their contribution to the global error. We advocate controlling the variance of the one-step errors, conditional on knowledge o...

We show that spectral functions relevant for commonly used models of the non-Debye relaxation are related to Stieltjes supported on positive semiaxis. Using only this property it can be shown response and nonnegative. They connected each other obey time evolution provided by integral equations involving memory function $M(t)$ which is as well. This fact also due character function. Stochastic p...

The-calculus with multiplicities is a reenement of the lazy-calculus where the argument in an application comes with a multiplicity, which is an upper bound to the number of its uses. This introduces potential deadlocks in the evaluation. We study the discriminating power of this calculus over the usual-terms. We prove in particular that the observational equivalence induced by contexts with mu...

We consider models for stock prices which relates to random pro cesses with independent homogeneous increments Levy processes These models are arbitrage free but correspond to the incomplete nancial market There are many di erent approaches for pricing of nancial derivatives We consider here mainly the approach which is based on minimal relative entropy This method is related to an utility func...

Edwards et al. 1 revisited well-known studies reporting power-laws in the frequency distribution of flight duration of wandering albatrosses 2,3 , and concluded that no Lévy process 4,5 could model recent observations with higher resolution. Here we show that this re-analysis 1 suffers from a conceptual misunderstanding, and that the new albatross data remain consistent with a biological Lévy f...