Neblux Knowledge Graph
Stochastic Processes
A stochastic process is an indexed family of random variables on one probability space. When the index represents time, a realization describes one possible time course.
Overview
For a Markov chain, the next-state distribution conditional on the past depends only on the present state. Standard Brownian motion, also called the Wiener process, starts at zero and has continuous paths with independent Gaussian increments of mean zero and variance equal to elapsed time.
Why it matters
Stochastic models can represent random arrivals and disturbances in state estimation. Predictions are distributions or estimates under a chosen model; using such a model does not by itself establish that physical uncertainty is irreducible.
What it builds on
Related concepts
- Natural SelectionappliedGenetic drift and mutation are stochastic processes that interact with deterministic selection in population genetics models
- Statistical InferenceappliedTime series analysis uses stochastic process models to make statistical inferences about temporal data and forecast future values
- Signal ProcessingappliedSignal processing models noise as stochastic processes to optimally filter and extract information from corrupted measurements
- MathematicslogicalStochastic Processes provides conceptual grounding that helps explain Mathematics in this knowledge graph.