Martingale (probability theory) — For the martingale betting strategy , see martingale (betting system). Stopped Brownian motion is an example of a martingale. It can be used to model an even coin toss betting game with the possibility of bankruptcy. In probability theory, a… … Wikipedia
Doob's martingale inequality — In mathematics, Doob s martingale inequality is a result in the study of stochastic processes. It gives a bound on the probability that a stochastic process exceeds any given value over a given interval of time. As the name suggests, the result… … Wikipedia
Doob-Meyer decomposition theorem — The Doob Meyer decomposition theorem is a theorem in stochastic calculus stating the conditions under which a submartingale may be decomposed in a unique way as the sum of a martingale and a continuous increasing process. It is named for J. L.… … Wikipedia
Doob decomposition theorem — In the theory of discrete time stochastic processes, a part of the mathematical theory of probability, the Doob decomposition theorem gives a unique decomposition of any submartingale as the sum of a martingale and an increasing predictable… … Wikipedia
Itō calculus — Itō calculus, named after Kiyoshi Itō, extends the methods of calculus to stochastic processes such as Brownian motion (Wiener process). It has important applications in mathematical finance and stochastic differential equations.The central… … Wikipedia
Paul-André Meyer — (21 August 1934 30 January 2003) was a French mathematicianHe is best known for his continuous time analog of Doob s decomposition of a submartingale, known as the Doob Meyer decomposition. Some of his main areas of research in probability theory … Wikipedia
Tanaka's formula — In the stochastic calculus, Tanaka s formula states that:|B t| = int 0^t sgn(B s) dB s + L twhere B t is the standard Brownian motion, sgn denotes the sign function:sgn (x) = egin{cases} +1, x geq 0; 1, x < 0. end{cases}and L t is its local time … Wikipedia
Alexandra Bellow — (1935 ndash;) is a mathematician who has made substantial contributions to the fields of ergodic theory, probability and analysis. BiographyShe was born in Bucharest, Romania, as Alexandra Bagdasar. Her parents were both physicians. Her mother,… … Wikipedia
Counting process — A counting process is a stochastic process {N(t), t ≥ 0} that possesses the following properties: N(t) ≥ 0. N(t) is an integer. If s ≤ t then N(s) ≤ N(t). If s < t, then N(t) − N(s) is the number of events occurred during the… … Wikipedia
Doob–Meyer decomposition theorem — The Doob–Meyer decomposition theorem is a theorem in stochastic calculus stating the conditions under which a submartingale may be decomposed in a unique way as the sum of a martingale and a continuous increasing process. It is named for J. L.… … Wikipedia
