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Stochastic Processes Overview
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Filtering
A methodology for estimating the hidden states in a stochastic process given noisy observations.
Stationary Process
A stochastic process whose statistical properties do not change over time.
Poisson Process
A stochastic process with independent increment events occurring at a constant average rate.
Itô's Lemma
A formula used to determine the stochastic differential of a function of a stochastic process.
Stochastic Process
A collection of random variables indexed by time or space, representing systems subject to random changes.
Levy Process
A stochastic process characterized by stationary and independent increments, generalizing random walks and Brownian motion.
Brownian Motion
A continuous-time stochastic process characterized by continuous paths and no memory, used to model random motion of particles in fluids.
Markov Property
A stochastic process property where future states depend only on the current state, not on the sequence of events that preceded it.
Wiener Process
Another name for Brownian Motion, a continuous-time process used in mathematical finance and physics.
Martingale
A model of a fair game where the conditional expected value of the next observation, given the past observations, is equal to the present observation.
Ergodicity
A property indicating that the time averages of a process converge to the ensemble averages as time approaches infinity.
Random Walk
A stochastic process that describes a path consisting of a succession of random steps.
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