Stokastiska

Stokastiska is a term used in Swedish to describe phenomena, models or processes that involve randomness and probability. In statistics and probability theory, a stokastisk modell or stokastisk process describes systems whose evolution is not completely determined by initial conditions but is influenced by random variation. A stokastisk process is a family of random variables indexed by time or another parameter, describing the state of a system at each moment. Unlike deterministic models, stokastiska modeller yield different outcomes under the same starting conditions, and their results are described using probability distributions, expectations and variances.

Key concepts in stokastiska modeller include sources of randomness, dependence and independence between variables, and the idea of information flow over time, such as filtrations and adapted processes in continuous time. Important classes of stokastiska processer include Markov chains (memoryless processes), Brownian motion (Wiener process), and Poisson processes (random events in time). Stokastisk calculus, particularly Itô calculus, provides mathematical tools to integrate with respect to stokastiska processer and to formulate stochastic differential equations that model systems under random influence.

Applications of stokastiska modeller are wide-ranging. In finance, stokastiska models underpin option pricing and risk management. In physics and engineering, they describe diffusion and noise-driven dynamics. In operations research, queueing theory uses stochastic models to analyze service systems. In ecology and epidemiology, randomness is essential for modelling population dynamics and the spread of diseases. Practically, stokastiska modelling is often complemented by numerical methods such as Monte Carlo simulation to estimate distributions and expectations when analytical solutions are not available.