We present in this article a game of chance (Saint Petersburg Paradox) and
generalize it on a probability space as an example of a previsible (predictable) process,
from which we get a discrete stochastic integration (DSI). Then we define a marting
ale
and present it as a good integrator of a discrete stochastic integration ∫ , which is
called the martingale transform of by such that is a previsible process.
After that we present the most important properties of the DSI, which include that the
DSI is also a martingale , the theorem of stability for it, the definition of the covariation of
two given martingales and the proof that the DSI is centered with a specific given variance.
Finally, we define Doob-decomposition and the quadratic variation and present Itȏformula
as a certain sort of it.
Van Tijm and Victor Gremonsky, in their comparative monetary work, have
established two closely related, largely divergent approaches and research methods. The
first to follow the approach of EvelFeilmann to look at international literary relations
is a
certain historical causation (historical theory). And the second approach to the theory of
typology, influenced by the writings of A. Vesilowski monetary, influenced by German
philosophers, starting in the second half of the eighteenth century. The term similarities
and differences between literatures is presented as a result of similarity or difference in the
movement of the development of societies and their conditions.
However, their divergence in principle did not override their agreement on some
partial issues and their divergence in other matters. This is what the research will try to
look at, using extrapolation as a means to elucidate judgments, which were ignored by
scholars and interested parties, in the hope of giving each person the right, both impartially
and objectively, to adopt their texts.
