Category: Stochastic calculus

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