Stochastic Processes

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20 domain-specific abstractions whose origin domain is Stochastic Processes.

• Asymmetric simple exclusion process — A continuous-time interacting-particle model on a lattice where biased nearest-neighbor jumps occur only into vacant sites.
• Brownian meander — A Brownian-motion-derived stochastic process on a fixed interval conditioned to remain nonnegative after leaving zero.
• Compound Poisson process — A jump process formed by summing independent random jump sizes at event times of a Poisson counting process.
• Continuous-time Markov chain — A stochastic process with the Markov property on a discrete state space whose state changes occur in continuous time according to exponential holding rates and transition intensities.
• Ergodic process — A stochastic process for which specified long-run time averages along almost every realization equal the corresponding ensemble expectations, allowing one sufficiently long trajectory to represent the regime.
• Excursion probability — The probability that a stochastic process crosses a specified threshold somewhere over a declared index region.
• Fano factor — A count-dispersion ratio equal to variance divided by mean, with one marking a Poisson baseline.
• Filtering problem (stochastic processes) — The sequential inference problem of estimating a hidden stochastic state from noisy partial observations available up to the present time.
• Gamma process — A nondecreasing Levy process with independent stationary increments distributed according to a gamma law, used to model cumulative random growth, wear, or activity.
• Generalized Wiener process — A continuous-time diffusion formed by adding state- or time-dependent drift and volatility to Brownian noise, commonly written as a stochastic differential equation.
• Kramers–Moyal expansion — An expansion of a Markov process master equation into an infinite series of state derivatives weighted by conditional jump moments.
• Local martingale — A stochastic process that becomes a martingale when stopped along an increasing sequence of stopping times tending to the time horizon.
• Palm calculus — The probability calculus relating a stationary point process as seen from a typical event to its ordinary time- or space-average law.
• Progressively measurable process — A stochastic process whose restriction through every time t is jointly measurable with respect to Borel time and the information available by t.
• Random measure — A measure-valued random element or kernel that assigns each outcome a locally finite measure, unifying random point configurations and stochastic mass distributions.
• Reflected Brownian motion — A Brownian diffusion constrained to a domain by a regulating process that pushes sample paths inward whenever they reach the boundary.
• Stationary process — A stochastic process whose probabilistic law is invariant under shifts of its time index, with weaker forms preserving selected moments instead.
• Stochastic drift — The systematic time-directed component of a stochastic process, commonly represented by the conditional mean rate of change apart from random fluctuation.
• Stopping time — A random time whose occurrence can be determined from information available up to that time, without access to future states of the stochastic process.
• Transition-rate matrix — The infinitesimal generator of a finite-state continuous-time Markov chain, with nonnegative off-diagonal jump rates and rows summing to zero.