Nature: Phylogenetic beta diversity in bacterial assemblages across ecosystems: deterministic versus stochastic processes
Phylogenetic beta diversity in bacterial assemblages across ecosystems: deterministic versus stochastic processes
What's the difference between stochastic and random? There is an anecdote about the notion of stochastic processes. They say that when Khinchin wrote his seminal paper "Correlation theory for stationary stochastic processes", this did not go well with Soviet authorities. The reason is that the notion of random process used by Khinchin contradicted dialectical materialism. In diamat, all ...
Finextra: Risk and portfolio management advanced approaches for Implementing Stochastic Correlation Processes
A stochastic process is a colection of random variables defined on the same probability space. Please explain further what parts of this definition are escaping you.
A transition matrix $P$ is said to be doubly stochastic if the sum over each column equals one, that is $\sum_i P_{ij}=1\space\forall i$. If such a chain is ...
I'm reading Karatzas + Shreve, Brownian Motion and Stochastic Calculus. The definition for measurability is given in 1.6: The stochastic process $X$ is called ...
Stochastic Calculus for Finance I: Binomial asset pricing model and Stochastic Calculus for Finance II: tochastic Calculus for Finance II: Continuous-Time Models. These two books are very good if you want to apply the theory to price derivatives. Stochastic Differential Equations: An Introduction with Applications Bernt Oksanda.
Affine processes provide a versatile framework for modelling complex financial phenomena, ranging from interest rate dynamics to credit risk and beyond. Their defining characteristic is the affine, or ...
Increasing evidence has emerged for non-random spatial distributions of microbes, but knowledge of the processes that cause variation in microbial assemblage among ecosystems is lacking. For instance, ...