Table Of Contents
  • Markov processes
  • Poisson processes
  • Brownian motion
  • Dynkin's formula
  • Blumenthal's 0-1 law

Markov processes

Markov process, also popularly known as the Markoff process, is used to satisfy the Markov property. The Markov processes are random processes where the outcome of one outcome is dependent on the results of the previous events. These processes are comprised of Feller, affine processes, diffusion, and other concepts. It is popularly used in analyzing the behavior of a variable in a project now or forecasting the project's behavior in the future.

Poisson processes

These are discrete events in which the average occurrence time between the events is well known. This is even though the timing of the events is random. The occurrence of an event in the Poisson distribution does not depend on another event's occurrence. Events only meet the Poisson criteria if they are proven to depend on each other.

Brownian motion

Brownian motion, which is also known as Pedesi, is the random movement of particles available in a gas or fluid, resulting in fast movement of molecules in that particular fluid. The Brownian motion explains a substance's movement from high concentration regions to regions of low concentration. The theory of Brownian motion proved that molecules and atoms actually existed.

Dynkin's formula

Dynkin's formula gives the correct value of smooth statistics of a specific lto diffusion when the even stops. Dynkin's formula is named after a popular Russian mathematician called Eugene Dynkin. Dynkin's formula is the counterpart to the deterministic process in stochastic.

Blumenthal's 0-1 law

This law explains the nature of starting memoryless processes. It explains the nature of the beginnings of the right continuous feller process. It notes that every right continuous feller process from a deterministic point has a deterministic earlier movement.