In the theory of stochastic processes, a subdiscipline of probability theory, filtrations are totally ordered collections of subsets that are used to model...

_{2}}.} Natural filtration Filtration (probability theory) Filter (mathematics) Björk, Thomas (2005). "Appendix B". Arbitrage Theory in Continuous Time...

In probability theory, a martingale is a stochastic process in which the expected value of the next observation, given all prior observations, is equal...

an ultrafilter is a limit point. Filtration (mathematics) – Indexed set in mathematics Filtration (probability theory) – Model of information available...

In probability theory and related fields, a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random...

topological notions and results. Filtration (mathematics) – Indexed set in mathematics Filtration (probability theory) – Model of information available...

law. Smoluchowski's theory of Brownian motion starts from the same premise as that of Einstein and derives the same probability distribution ρ(x, t)...

the solution is required to be adapted with respect to an underlying filtration. BSDEs naturally arise in various applications such as stochastic control...

In the theory of stochastic processes in mathematics and statistics, the generated filtration or natural filtration associated to a stochastic process...

process which generates them. The theory of random graphs lies at the intersection between graph theory and probability theory. From a mathematical perspective...

{F}}_{t})_{t\geq 0},\mathbb {P} )} be a filtered probability space and M {\displaystyle M} be a smooth manifold. The filtration satisfies the usual conditions, i.e...

In mathematical analysis and in probability theory, a σ-algebra ("sigma algebra") is part of the formalism for defining sets that can be measured. In calculus...

In probability theory, the optional stopping theorem (or sometimes Doob's optional sampling theorem, for American probabilist Joseph Doob) says that, under...

This is a list of integration and measure theory topics, by Wikipedia page. Length Area Volume Probability Moving average Riemann sum Riemann–Stieltjes...

In probability theory, Novikov's condition is the sufficient condition for a stochastic process which takes the form of the Radon–Nikodym derivative in...

lists articles related to probability theory. In particular, it lists many articles corresponding to specific probability distributions. Such articles...

In the mathematical theory of probability, a Doob martingale (named after Joseph L. Doob, also known as a Levy martingale) is a stochastic process that...

that is found in general topology Filtration (mathematics) – Indexed set in mathematics Filtration (probability theory) – Model of information available...

In probability theory, the martingale representation theorem states that a random variable with finite variance that is measurable with respect to the...

to random walk and filtration of the random processes { X t } 0 ∞ {\displaystyle \{X_{t}\}_{0}^{\infty }} . In probability theory innovation series is...

In probability theory and statistics, the term Markov property refers to the memoryless property of a stochastic process, which means that its future evolution...

In probability theory, a real-valued stochastic process X is called a semimartingale if it can be decomposed as the sum of a local martingale and a càdlàg...

lattice components in the filtration problem that modulates capacity for percolation. During the last decades, percolation theory, the mathematical study...

In probability theory, in particular in the study of stochastic processes, a stopping time (also Markov time, Markov moment, optional stopping time or...

In mathematics and probability theory, Skorokhod's embedding theorem is either or both of two theorems that allow one to regard any suitable collection...

transport the sample through the column, the technique is known as gel filtration chromatography, versus the name gel permeation chromatography, which is...

examples of direct and inverse systems are the ones arising from filtrations in probability theory, and the limits and colimits of such systems are, respectively...

inequality is a submartingale relative to a filtration of the underlying probability space. The probability measure on the sample space of the martingale...

product e-variables form a nonnegative discrete-time martingale in the filtration generated by Y ( 1 ) , Y ( 2 ) , … {\displaystyle Y_{(1)},Y_{(2)},\ldots...

In probability theory, Girsanov's theorem or the Cameron-Martin-Girsanov theorem explains how stochastic processes change under changes in measure. The...