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- Stochastic calculus

H-derivative

In mathematics, the H-derivative is a notion of derivative in the study of abstract Wiener spaces and the Malliavin calculus.

Palm calculus

In the study of stochastic processes, Palm calculus, named after Swedish teletrafficist Conny Palm, is the study of the relationship between probabilities conditioned on a specified event and time-ave

Chapman–Kolmogorov equation

In mathematics, specifically in the theory of Markovian stochastic processes in probability theory, the Chapman–Kolmogorov equation is an identity relating the joint probability distributions of diffe

Itô's lemma

In mathematics, Itô's lemma or Itô's formula (also called the Itô-Doeblin formula, especially in French literature) is an identity used in Itô calculus to find the differential of a time-dependent fun

Stochastic logarithm

In stochastic calculus, stochastic logarithm of a semimartingale such that and is the semimartingale given by In layperson's terms, stochastic logarithm of measures the cumulative percentage change in

Quantum stochastic calculus

Quantum stochastic calculus is a generalization of stochastic calculus to noncommuting variables. The tools provided by quantum stochastic calculus are of great use for modeling the random evolution o

Integration by parts operator

In mathematics, an integration by parts operator is a linear operator used to formulate integration by parts formulae; the most interesting examples of integration by parts operators occur in infinite

Stratonovich integral

In stochastic processes, the Stratonovich integral (developed simultaneously by Ruslan Stratonovich and ) is a stochastic integral, the most common alternative to the Itô integral. Although the Itô in

Malliavin derivative

In mathematics, the Malliavin derivative is a notion of derivative in the Malliavin calculus. Intuitively, it is the notion of derivative appropriate to paths in classical Wiener space, which are "usu

Ornstein–Uhlenbeck operator

In mathematics, the Ornstein–Uhlenbeck operator is a generalization of the Laplace operator to an infinite-dimensional setting. The Ornstein–Uhlenbeck operator plays a significant role in the Malliavi

Itô calculus

Itô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical finance and st

Malliavin calculus

In probability theory and related fields, Malliavin calculus is a set of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic functions to

Pricing kernel

No description available.

Fokker–Planck equation

In statistical mechanics, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of the velocity of a particle under the in

State price density

No description available.

Tanaka's formula

In the stochastic calculus, Tanaka's formula states that where Bt is the standard Brownian motion, sgn denotes the sign function and Lt is its local time at 0 (the local time spent by B at 0 before ti

Skorokhod problem

In probability theory, the Skorokhod problem is the problem of solving a stochastic differential equation with a reflecting boundary condition. The problem is named after Anatoliy Skorokhod who first

White noise analysis

In probability theory, a branch of mathematics, white noise analysis, otherwise known as Hida calculus, is a framework for infinite-dimensional and stochastic calculus, based on the Gaussian white noi

Kramers–Moyal expansion

In stochastic processes, Kramers–Moyal expansion refers to a Taylor series expansion of the master equation, named after Hans Kramers and José Enrique Moyal. This expansion transforms the integro-diff

Itô isometry

In mathematics, the Itô isometry, named after Kiyoshi Itô, is a crucial fact about Itô stochastic integrals. One of its main applications is to enable the computation of variances for random variables

Skorokhod integral

In mathematics, the Skorokhod integral, often denoted , is an operator of great importance in the theory of stochastic processes. It is named after the Ukrainian mathematician Anatoliy Skorokhod. Part

Paley–Wiener integral

In mathematics, the Paley–Wiener integral is a simple stochastic integral. When applied to classical Wiener space, it is less general than the Itō integral, but the two agree when they are both define

Master equation

In physics, chemistry and related fields, master equations are used to describe the time evolution of a system that can be modelled as being in a probabilistic combination of states at any given time

Stochastic discount factor

The concept of the stochastic discount factor (SDF) is used in financial economics and mathematical finance. The name derives from the price of an asset being computable by "discounting" the future ca

Reflection principle (Wiener process)

In the theory of probability for stochastic processes, the reflection principle for a Wiener process states that if the path of a Wiener process f(t) reaches a value f(s) = a at time t = s, then the s

Stochastic calculus

Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to s

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