Stochastic processes

mathematical object usually defined as a collection of random variables

mathematical formalization of a path that consists of a succession of random steps

Stochastic (; ) is the property of being well-described by a random probability distribution. Stochasticity and randomness are technically distinct concepts. Stochasticity refers to a modeling approach, while randomness describes phenomena. These terms are often used interchangeably. In probability theory, the formal concept of a stochastic process is also referred to as a random process.

stochastic process whose unconditional joint probability distribution does not change when shifted in time

notions of probabilistic convergence, applied to estimation and asymptotic analysis

model in probability theory, used in gambling

differential equations involving stochastic processes

partial differential equation

stochastic process such that every finite collection of random variables has a multivariate normal distribution

random process of binary (boolean) random variables

In mathematics, a càdlàg (), RCLL ("right continuous with left limits"), or corlol ("continuous on (the) right, limit on (the) left") function is a function defined on the real numbers (or a subset of them) that is everywhere right-continuous and has left limits everywhere. Càdlàg functions are important in the study of stochastic processes that admit (or even require) jumps, unlike Brownian motion, which has continuous sample paths. The collection of càdlàg functions on a given domain is known as Skorokhod space.

formula relating stochastic processes to partial differential equations

type of noise in signal processing

specific type of “random time”: a random variable whose value is interpreted as the time at which a given stochastic process exhibits a certain behavior of interest

theorem

signal boosting phenomenon using white noise

probability model, originally to model the extinction of family names

financial theory

probabilistic inequality of partial sums of independent random variables

theorem

indexed set of subobjects of an algebraic structure

Stochastic process

conformally invariant stochastic process

stochastic process associated with semimartingale processes such as Brownian motion

randomized mathematical sequence based upon the Fibonacci sequence

discrete-time stochastic process

quantity defined for a stochastic process; its finiteness ensures that stochastic calculus works properly

stochastic process with values that are nondecreasing nonnegative integers

stochastic process

subfield of control theory

separable Banach space equipped with a Hilbert subspace such that the standard cylinder set measure on the Hilbert subspace induces a Gaussian measure on the whole Banach space

Measure in measure theory

stochastic process used in biology to describe finite populations

The numéraire (or numeraire) is a basic standard by which value is computed. In mathematical economics it is a tradable economic entity in terms of whose price the relative prices of all other tradables are expressed. In a monetary economy, one of the functions of money is to act as the numéraire, i.e. to serve as a unit of account and therefore provide a common benchmark relative to which the value of various goods and services can be measured against.

frequency-domain analysis method

computer simulation with random inputs

stochastic process with discrete movements

mathematical process for stochastic differential equations

continuous in probability stochastic process with independent increments

property in the mathematical theory of stochastic processes

concept in statistical mechanics