probability theory, a continuous stochastic process is a type of stochastic process that may be said to be "continuous" as a function of its "time" or index parameter...

theory and statistics, a continuous-time stochastic process, or a continuous-space-time stochastic process is a stochastic process for which the index variable...

of stochastic processes are respectively referred to as discrete-time and continuous-time stochastic processes. Discrete-time stochastic processes are...

process (or Brownian motion, due to its historical connection with the physical process of the same name) is a real-valued continuous-time stochastic...

calculus to stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical finance and stochastic differential...

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution...

Feller-continuous process is a continuous-time stochastic process for which the expected value of suitable statistics of the process at a given time in the...

In probability theory, a Lévy process, named after the French mathematician Paul Lévy, is a stochastic process with independent, stationary increments:...

a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion (also called a Wiener process) with...

{F}},({\mathcal {F}}_{t})_{t\geq 0},\mathbb {P} )} , then a continuous-time stochastic process ( X t ) t ≥ 0 {\displaystyle (X_{t})_{t\geq 0}} is predictable...

P(t=0)=\alpha } . Continuous-time stochastic process Continuous function Continuous geometry Continuous modelling Continuous or discrete spectrum Continuous spectrum...

diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion process is stochastic in nature...

process, also called the Brownian motion process. One of the simplest continuous-time stochastic processes is Brownian motion. This was first observed...

process, a continuous-time stochastic process Process calculus, a diverse family of related approaches for formally modeling concurrent systems Process function...

a stationary process (also called a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose statistical...

A continuous-time Markov chain (CTMC) is a continuous stochastic process in which, for each state, the process will change state according to an exponential...

compound Poisson process is a continuous-time stochastic process with jumps. The jumps arrive randomly according to a Poisson process and the size of the...

Markov decision process (MDP), also called a stochastic dynamic program or stochastic control problem, is a model for sequential decision making when...

In probability theory, the telegraph process is a memoryless continuous-time stochastic process that shows two distinct values. It models burst noise (also...

probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability...

process Branching process Branching random walk Brownian bridge Brownian motion Chinese restaurant process CIR process Continuous stochastic process Cox...

The context may be either discrete time or continuous time. An extremely well-studied formulation in stochastic control is that of linear quadratic Gaussian...

In mathematics, the Ornstein–Uhlenbeck process is a stochastic process with applications in financial mathematics and the physical sciences. Its original...

In mathematics, a sample-continuous process is a stochastic process whose sample paths are almost surely continuous functions. Let (Ω, Σ, P) be a probability...

modeled mathematically by means of the telegraph process, a Markovian continuous-time stochastic process that jumps discontinuously between two distinct...

wandering particle waits for a random time between jumps. It is a stochastic jump process with arbitrary distributions of jump lengths and waiting times...

A jump process is a type of stochastic process that has discrete movements, called jumps, with random arrival times, rather than continuous movement, typically...

autoregressive integrated moving average (ARIMA) models of time series, which have a more complicated stochastic structure; it is also a special case of the vector...

wealth in terms of continuous-time stochastic processes. Under this model, these assets have continuous prices evolving continuously in time and are driven...

A stochastic simulation is a simulation of a system that has variables that can change stochastically (randomly) with individual probabilities. Realizations...