MSP15 - Geometric probabilities, stochastic process and applications to sciences

The study of Probability is a relatively recent development in the history of Mathematics. Two French mathematicians Blaise Pascal (1623-1662) and Pierre De Fermat (1601-1665) founded Mathematical Probability in the mid-17th cen- tury. Their early discoveries regarded the probability of games with dice and cards. From their original studies on the subject, the study of Probability devel- oped into a modern theory with applications in various elds. Probability prob- lems originating from real situations can be resolved using Geometry. Recently, the classical Buon's needle problem, regarding the calculation of the probabil- ity that a needle will intersect a line if thrown at random onto a Euclidean plane ruled by parallel lines, has been extended to consider the probability of intersec- tion with dierent grids having a polygon as their fundamental cell, throwing a needle or a dierent test body, such as a rectangle or a circle. Problems of the same kind can be studied in the Euclidean space. These originate from various situations: in the calculation of the probability that a meteorite will strike a certain area, in the eld of transport in the calculation of the probability that a train will pass through a certain number of stations. For situations of this kind we can make a geometric framework and resolve the problem of probabil- ity using geometry. In this new mini symposium certain results of Geometric Probability by M. Stoka will be generalized. Moreover, Buon and Laplace type problems for regular grids with obstacles will be considered. 2