Stokastiikan

Stokastiikan is a term used in Finnish-language mathematical literature to denote the study of stochastic processes and their applications. It concerns the mathematical analysis of systems influenced by randomness, using probability spaces, random variables, and models that evolve over time. The field emphasizes both theoretical foundations and practical modeling of uncertainty.

Core concepts include stochastic processes such as Markov chains, renewal processes, and Brownian motion, as well as martingales and stochastic integrals. Techniques involve probability theory, stochastic calculus (Itô and Stratonovich integrals), differential equations driven by randomness, and numerical methods such as Monte Carlo simulation for estimating properties of complex models.

Applications of stokastiikan span finance, physics, engineering, and biology. In finance, stochastic models underpin option pricing, risk assessment, and asset dynamics. In physics, they describe particle diffusion and random media. In engineering and biology, they are used to model noise, population dynamics, and gene expression variability.

Historically, stokastiikan develops from the broader theory of probability in the 20th century, with contributions from mathematicians such as Norbert Wiener and Andrey Kolmogorov, and later advances in stochastic calculus and numerical simulation enabling real-world applications. Related topics include stochastic processes, probability theory, stochastic calculus, and time series analysis.