Search results

...al]] of a [[local martingale]] is a true [[Martingale (probability theory)|martingale]]. This is particularly important if [[Girsanov theorem|Girsanov's theorem] ...n the Doléans-Dade exponential ''Ɛ''(''M'') of M is a uniformly integrable martingale. ...

In [[probability theory]], the '''minimal-entropy martingale measure (MEMM)''' is the risk-neutral probability measure that minimises th ...minimises the variance of the equivalent [[martingale (probability theory)|martingale]]. For certain situations, the resultant measure <math>Q</math> will not be ...

{{Short description|Exponential martingale associated to sum of iid variables}} ...gale''' is the name sometimes given to a [[Martingale_(probability_theory)|martingale]] used to study sums of [[Independent and identically distributed random va ...

...d [[information theory]] of [[probability theory|probability]], a '''sigma-martingale''' is a [[semimartingale]] with an integral representation. Sigma-martinga ...ists an <math>\mathbb{R}^d</math>-valued [[martingale (probability theory)|martingale]] ''M'' and an ''M''-[[Ito integral|integrable]] [[predictable process]] <m ...

In [[probability theory]], '''Ville's inequality''' provides an [[upper bound]] on the [[probabilit | title=Probability Theory and Examples ...

...}</ref><ref>{{cite book|title=Markets with Transaction Costs: Mathematical Theory|url=https://archive.org/details/marketswithtrans00kaba|url-access=limited|a The CPP plays the role of an [[equivalent martingale measure]] in markets with [[transaction costs]].<ref>{{cite journal|title=N ...

In [[Martingale (probability theory)|martingale theory]], '''Émery topology''' is a [[topology]] on the space of [[semimartingale] ...ega,\mathcal{A},\{\mathcal{F_t}\},P)</math> be a [[Filtration (probability theory)|filtered]] probability space, where the filtration satisfies the [[usual c ...

...s–Dubins–Schwarz theorem''') is a theorem that says all continuous [[local martingale]]s and martingales are time-changed [[Brownian motion]]s. ...E.|last=Dambis|title=On decomposition of continuous submartingales|journal=Theory of Probability and Its Applications|volume=10|date=1965|issue=3 |pages=401– ...

In [[stochastic analysis]], a part of the mathematical theory of [[probability]], a '''predictable process''' is a [[stochastic process]] * [[Martingale (probability theory)|Martingale]] ...

{{Short description|A martingale's expected value at a stopping time equals its initial expected value}} ...sary for this result to hold true. In particular, the theorem applies to [[Martingale (betting system)|doubling strategies]]. ...

...ahrscheinlichkeitstheorie und Verwandte Gebiete |trans-journal=Probability Theory and Related Fields|language=fr|volume=16|issue=3|pages=181–194|doi=10.1007/ * Stochastic exponential of a local martingale is again a local martingale. ...

...Strong law|Strong Law of Large Numbers]].<ref>Durrett, Rick. "Probability: Theory and Examples." Duxbury advanced series, Third Edition, Thomson Brooks/Cole, ...(1963) pp. Sect. 16.3</ref><ref>W. Feller, "An introduction to probability theory and its applications", 2, Wiley (1971) pp. Sect. IX.9</ref> ...

...ble]] stochastic process as the sum of a [[Martingale (probability theory)|martingale]] and a [[predictable process]] (or "drift") starting at zero. The theorem ...b>n</sub>''{{!}}] < ∞}} for all {{math|''n'' ∈ ''I''}}. Then there exist a martingale {{math|1=''M'' = (''M_n'')_{''n''∈''I''}}} and an integra ...

...ath>V</math> with respect to a family of [[Risk-neutral measure|equivalent martingale measure]]s into the form ...dging contingent claims in incomplete security markets|journal=Probability Theory and Related Fields|volume=105|pages=459–479|date=1996|doi=10.1007/BF0119190 ...

...e a favorable game. These names are suggested by probabilistic [[potential theory]], where martingales correspond to [[harmonic function]]s, supermartingales ...S002190020000019X}}</ref> Snell earned his Ph.D. in 1951 ("Applications of Martingale System Theorems"), with Doob as his supervisor. ...

In [[probability theory]], '''Bennett's [[inequality (mathematics)|inequality]]''' provides an [[up ...name=BLM2013>{{cite book|title=Concentration inequalities, a nonasymptotic theory of independence | first1=Stephane | last1=Boucheron | first2=Gabor|last2=Lu ...

...pendence]] that is weaker than the concept of a [[Martingale (probability)|martingale]]{{citation needed|date=May 2020}}. A (time) [[sequence]] of [[random vari ...9}} In particular, weak dependence is a natural condition for the ergodic theory of random functions.<ref>{{Cite journal|last1=Wu|first1=Wei Biao|authorlink ...

...949) and Anderson and Darling (1952),<ref>{{cite journal |title=Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes |first= ...d to replace the parametric empirical process <math>\hat v_n</math> by its martingale part <math>w_n</math> only. ...

If <math>\xi\in L^2(\Omega,\mathbb{P})</math>, then it follows from the [[martingale representation theorem]], that there exists a unique stochastic process <ma * [[Martingale representation theorem]] ...

...convexity adjustment arises from the [[Jensen inequality]] in probability theory: the expected value of a convex function is greater than or equal to the fu ...ng financial variables modeled are not a [[Martingale_(probability_theory)|martingale]] under the [[Risk-neutral measure|pricing measure]]. ...