Paris Bourse in the context of "Amsterdam Stock Exchange"

In probability theory and related fields, a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance.

Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownian motion process, used by Louis Bachelier to study price changes on the Paris Bourse, and the Poisson process, used by A. K. Erlang to study the number of phone calls occurring in a certain period of time. These two stochastic processes are considered the most important and central in the theory of stochastic processes, and were invented repeatedly and independently, both before and after Bachelier and Erlang, in different settings and countries.

The 2nd arrondissement of Paris (II arrondissement) is one of the 20 arrondissements of the capital city of France. In spoken French, this arrondissement is colloquially referred to as deuxième (second/the second). It is governed locally together with the 1st, 3rd and 4th arrondissement, with which it forms the 1st sector of Paris.

Also known as Bourse, this arrondissement is located on the right bank of the River Seine. The 2nd arrondissement, together with the adjacent 8th and 9th arrondissements, hosts an important business district, centred on the Paris Opéra, which houses the city's most dense concentration of business activities. The arrondissement contains the former Paris Bourse (stock exchange) and several banking headquarters, as well as a textile district, known as the Sentier, and the Opéra-Comique's theatre, the Salle Favart. The 2nd arrondissement is the home of Grand Rex, the largest movie theater in Paris.

The Brussels Stock Exchange (French: Bourse de Bruxelles [buʁs də bʁysɛl]; Dutch: Beurs van Brussel [ˈbøːrs fɑm ˈbrʏsəl]), abbreviated to BSE, was founded in Brussels, Belgium, by decree of Napoleon in 1801. In 2000, the BSE merged with the Amsterdam, Lisbon and Paris stock exchanges into Euronext, renaming the BSE Euronext Brussels. The benchmark stock market index on the BSE is the BEL 20.

The former Brussels Stock Exchange building, known as the Bourse Palace (French: Palais de la Bourse; Dutch: Beurspaleis) and usually shortened to la Bourse (in French) or de Beurs (in Dutch), is located on the Place de la Bourse/Beursplein along the Boulevard Anspach/Anspachlaan. The BSE is now headquartered in the Marquis building. It can be accessed from Brussels-Central railway station.