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In probability theory, an excursion probability is the probability that a stochastic process surpasses a given value in a fixed time period. It is the
Excursion_probability
Uncontrolled nuclear fission chain reaction
chain reaction. It is sometimes referred to as a critical excursion, critical power excursion, divergent chain reaction, or simply critical. Any such event
Criticality_accident
Stochastic process
In probability theory a Brownian excursion process (BPE) is a stochastic process that is closely related to a Wiener process (or Brownian motion). Realisations
Brownian_excursion
Diving mode and decompression technique
the effect of pressure variation due to excursions away from holding pressure, thereby reducing the probability and amount of bubble formation due to these
Saturation_diving
Formula in probability theory
an excursion probability ℙ{supt∈[0,1]X(t)≥u} as for large values of u the probability that there is a level crossing is approximately the probability of
Rice's_formula
Two closely related models for generating random graphs
David (1997-04-01). "Brownian excursions, critical random graphs and the multiplicative coalescent". The Annals of Probability. 25 (2). doi:10.1214/aop/1024404421
Erdős–Rényi_model
Hypothesis test in mathematics
The sequential probability ratio test (SPRT) is a specific sequential hypothesis test, developed by Abraham Wald and later proven to be optimal by Wald
Sequential probability ratio test
Sequential_probability_ratio_test
Book by Claude Dellacherie and Paul-André Meyer
Probabilities and Potential (titled Probabilités et Potentiel in the original French) is a mathematics book written by Claude Dellacherie and Paul-André
Probabilities_and_Potential
Gaussian process pinned at both ends
such as the Brownian excursion. The law of B is that of a standard Brownian motion W conditioned on W(1)=0. This event has probability zero, but the conditional
Brownian_bridge
Concept in probability theory
Vervaat, W. (1979). "A relation between Brownian bridge and Brownian excursion". Annals of Probability. 7 (1): 143–149. doi:10.1214/aop/1176995155.
Brownian_tree
Emeritus Professor of Statistics and Mathematics
(1992-03-01). "Size-biased sampling of Poisson point processes and excursions". Probability Theory and Related Fields. 92 (1): 21–39. doi:10.1007/BF01205234
Jim_Pitman
Stochastic process in probability theory
(1992). "Size-biased sampling of Poisson point processes and excursions". Probability Theory and Related Fields. 92: 21–39. doi:10.1007/BF01205234. Perman
Pitman–Yor_process
relational model Probability Probability bounds analysis Probability box Probability density function Probability distribution Probability distribution function
List_of_statistics_articles
Probability theory term
is formalized in probability theory by conditioning. Conditional probabilities, conditional expectations, and conditional probability distributions are
Conditioning_(probability)
French mathematician (1886-1971)
December 1971) was a French mathematician who was active especially in probability theory, introducing fundamental concepts such as local time, stable distributions
Paul_Lévy_(mathematician)
Collection of results for one-dimensional random walks and Brownian motion
"Brownian motion, bridge, excursion, and meander characterized by sampling at independent uniform times". Electronic Journal of Probability. 4: 1–33. doi:10.1214/EJP
Arcsine_laws_(Wiener_process)
Stochastic process generalizing Brownian motion
(1979). "A relation between Brownian bridge and Brownian excursion". Annals of Probability. 7 (1): 143–149. doi:10.1214/aop/1176995155. JSTOR 2242845
Wiener_process
Sequential model-based optimization of expensive black-box functions
measure of an excursion set. Stepwise uncertainty reduction strategies choose evaluations to reduce uncertainty about this probability, rather than to
Bayesian_optimization
Japanese mathematician (born 1935)
to probability theory, stochastic processes and stochastic differential equations. He is revered as a luminary in the field of modern probability theory
Shinzo_Watanabe
1889 train wreck in Armagh, Ireland
finding: This terrible calamity would in all human probability have been prevented had the excursion train been fitted with an automatic continuous brake
Armagh_rail_disaster
Reversal of direction of Earth's magnetic field
only a few hundred years (such as the Laschamp excursion). These events are classified as excursions rather than full geomagnetic reversals. Stable polarity
Geomagnetic_reversal
Concept in statistics
a Gaussian random field (GRF) is a random field involving Gaussian probability density functions of the variables. A one-dimensional GRF is also called
Gaussian_random_field
Probability distribution
The Tracy–Widom distribution is a probability distribution from random matrix theory introduced by Craig Tracy and Harold Widom (1993, 1994). It is the
Tracy–Widom_distribution
Heritage railway in Cumbria, England
connections that were established in 1869. During the summer season, excursion trains from Lancashire and elsewhere used the east-to-north side of Plumpton
Lakeside and Haverthwaite Railway
Lakeside_and_Haverthwaite_Railway
Welsh mathematician
David Williams FRS is a Welsh mathematician who works in probability theory. David Williams was born at Gorseinon, near Swansea, Wales. He was educated
David Williams (mathematician)
David_Williams_(mathematician)
Analytic function in mathematics
Pitman, Jim; Yor, Marc (2001). "Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions". Bulletin of the American
Riemann_zeta_function
French mathematician, statistician
Nathalie Eisenbaum is a French mathematician, statistician, and probability theorist. She works as a director of research with the Centre national de
Nathalie_Eisenbaum
many mathematical contexts, in particular geometric group theory and probability theory. They are also the simplest examples of Gromov hyperbolic spaces
Real_tree
Number, approximately 3.14
result that the probability of two random numbers being relatively prime (that is, having no shared factors) is equal to 6/π2. This probability is based on
Pi
Sustained nuclear fission achieved solely by prompt neutron emission
assembly is critical if every released neutron has a 1/2.43 = 0.41 = 41 % probability of causing another fission event as opposed to either being absorbed
Prompt_criticality
Swiss-American engineer and educator
taking colleagues and family out for excursions on the San Francisco Bay. On his many field trips and academic excursions, he took thousands of photographs
Hans_Albert_Einstein
14C BP) is in good agreement with the probability distribution function, indicating at a high level of probability that Neanderthals did not survive at
Neanderthal_extinction
Process in mathematical probability theory
(1977). "Weak convergence to Brownian meander and Brownian excursion". The Annals of Probability. 5 (1): 117–129. doi:10.1214/aop/1176995895. Revuz, Daniel;
Brownian_meander
Method for describing dice rolls
to discuss probability distribution in an article, "Dice as Random Number Generators", in the inaugural issue of fanzine Alarums & Excursions (1975). The
Dice_notation
Son of Pope Alexander VI (c. 1476 – 1497)
Rome. It was a sign of this friendship that they rode together during an excursion of the papal court through the city to Saint John Lateran on 5 May 1493
Giovanni Borgia, 2nd Duke of Gandía
Giovanni_Borgia,_2nd_Duke_of_Gandía
1972 book on parapsychology
ISSN 0007-1773. Gridgeman, N. T. (1975-01-01). "THE ROOTS OF COINCIDENCE: AN EXCURSION INTO PARAPSYCHOLOGY, Arthur Koestler". World Futures. 14 (3): 307–312
The_Roots_of_Coincidence
American mathematician (born 1981)
centers on arithmetic statistics, with excursions into related questions in arithmetic geometry and probability theory.[citation needed] Wood was born
Melanie_Wood
Bed of material at a runway's end to stop aircraft overrun
of runway excursions worldwide may turn out to be much more cost-effective than the current focus on reducing the already very low probability of occurrence
Engineered materials arrestor system
Engineered_materials_arrestor_system
1991 aircraft accident in Thailand
Klausen, Val Gardena, Olang, Mals and Kiens, who had participated in an excursion to the Far East under the guidance of Clemens August Andreae. The other
Lauda_Air_Flight_004
Volcanic eruption in New Zealand
the island at the time. Of these people, 38 were passengers on a shore excursion from the cruise ship Ovation of the Seas, which was on a 12-day voyage
2019 Whakaari / White Island eruption
2019_Whakaari_/_White_Island_eruption
Process by which atoms or molecules acquire charge by gaining or losing electrons
singly or multiply charged ions. The ionization rate, i.e. the ionization probability in unit time, can be calculated using quantum mechanics. (There are classical
Ionization
Solution to a stochastic differential equation
In probability theory and statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion
Diffusion_process
Number divisible only by 1 and itself
yes with probability at most 1/2 and no with probability at least 1/2. If this test is repeated n times on the same number, the probability that a composite
Prime_number
2018 video game
life. The development team had previously carried out a similar research excursion to Nepal during development of Far Cry 4. As the development team was
Far_Cry_5
American mathematician (1929–2017)
the University of California, San Diego. Getoor's research deals with probability theory, especially the theory of Markov processes and potential theory
Ronald_Getoor
Nuclear reactor where water boils in core
formation, making the neutron moderation less efficient and the fission probability lower. In normal operation, the control rods are only used to keep a
Boiling_water_reactor
British mathematician
Andreas E., eds. (2021). "A Lifetime of Excursions Through Random Walks and Lévy Processes". Progress in Probability. 78: 1–4. Retrieved 1 August 2025. Ron
Ron_Doney
Music genre that uses electronic instruments
music, which is a composing method that uses mathematical probability systems. Different probability algorithms were used to create a piece under a set of
Electronic_music
Stochastic processes in mathematics
of Doob's martingale convergence theorems. By bounding the probability of extreme excursions of the sample paths, it ensures that martingales with bounded
Doob's_martingale_inequality
Stochastic volatility model used in derivatives markets
payoff max ( F T − K , 0 ) {\displaystyle \max(F_{T}-K,\;0)} under the probability distribution of the process F t {\displaystyle F_{t}} . Except for the
SABR_volatility_model
Theorem in set theory
Arie (2013), Proofs of the Cantor-Bernstein theorem. A mathematical excursion, Science Networks. Historical Studies, vol. 45, Heidelberg: Birkhäuser/Springer
Schröder–Bernstein_theorem
French mathematician
Andreas E. (2021). "A Lifetime of Excursions Through Random Walks and Lévy Processes" (PDF). Progress in Probability. 78: 4. Retrieved 29 March 2025. Barlow
Jean_Bertoin
Severe events involving radioactive materials
A criticality accident (also sometimes referred to as an "excursion" or "power excursion") occurs when a nuclear chain reaction is accidentally allowed
Nuclear and radiation accidents and incidents
Nuclear_and_radiation_accidents_and_incidents
Third period of the Paleozoic Era
throughout the Silurian, evidenced by numerous major carbon and oxygen isotope excursions during this geologic period. Sea levels rose from their Hirnantian low
Silurian
Disorder caused by dissolved gases forming bubbles in tissues
harmlessly eliminated through respiration, or by decompression by an upward excursion from a condition of saturation by the inert breathing gas components,
Decompression_sickness
Statistical experiment designs
calculation of these probabilities, usually as a function of F ( x ) {\displaystyle F(x)} . Assuming that transition probabilities are fixed in time, depending
Up-and-down_design
Facility for supporting saturation diving projects
is stand-by diver to the working divers. Each diver is supplied by an excursion umbilical from inside the bell. The bell has a set of high pressure gas
Saturation_diving_system
Collision between a vehicle and a bird
the day during the bird migration season. Location affects bird strike probability since different bird species with distinct builds and behaviors reside
Bird_strike
1968 book by Robert M. Blumenthal and Ronald K. Getoor
compactification, Lévy systems, characteristic measures, the Martin boundary, and excursion theory. At 11:40 Getoor says "in the summer of [19]60 Blumenthal and I
Markov Processes and Potential Theory
Markov_Processes_and_Potential_Theory
Australian statistician (1927–2024)
time." Journal of Applied Probability 1, no. 2 (1964): 369–384. Hasofer, Abraham M. "Studies in the history of probability and statistics. XVI. Random
Michael_Hasofer
Process that eliminates all biological agents on an object or in a volume
calculated as an 8-hour time-weighted average (TWA) – and 5 ppm as a 15-minute excursion limit (EL). The National Institute for Occupational Safety and Health's
Sterilization_(microbiology)
Aborted Moon landing mission in the Apollo program
was designed to shut the engine down in response to chamber pressure excursions. Pogo oscillations had occurred on Titan rockets (used during the Gemini
Apollo_13
Joanna Russ The four protagonists move between parallel worlds using "probability travel". 1977– Xanth series Piers Anthony Xanth is a world governed by
List of fictional works featuring parallel universes
List_of_fictional_works_featuring_parallel_universes
Red dwarf star in the constellation Aquarius
simulations exist, such as the "Exoplanet Travel Bureau" and the "Exoplanets Excursion"—both by NASA. Scientific accuracy has been a point of discussion both
TRAPPIST-1
Branch of mathematics
Artists". Calculus training materials at imomath.com Archived 9 July 2023 at the Wayback Machine (in English and Arabic) The Excursion of Calculus, 1772
Calculus
Laurel Smith; Persi Diaconis (1988). "Honest bernoulli excursions". Journal of Applied Probability. 25 (3): 464–477. doi:10.2307/3213976. JSTOR 3213976
Brownian motion and Riemann zeta function
Brownian_motion_and_Riemann_zeta_function
Pitman, Jim; Yor, Marc (2001). "Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions". Bull. Amer. Math. Soc. (N
Lévy's_stochastic_area
Hovatter & Wilson Mantilla (2026). Evidence indicating that carbon isotope excursions and probable warming events during the Danian were associated with strong
2026_in_paleomammalogy
American jazz cornetist, pianist and composer (1903–1931)
stopped coming home for supper to hurry to the riverfront, slip aboard an excursion boat, and play the calliope. A friend remembered that Beiderbecke showed
Bix_Beiderbecke
US Marine Corps base in Hawaii
2023 - A Boeing P-8A Poseidon assigned to the VP-4 suffered a runway excursion and came to rest in Kāneʻohe Bay after attempting to land on runway 22
Marine Corps Air Station Kaneohe Bay
Marine_Corps_Air_Station_Kaneohe_Bay
Directed graph where each vertex pair has one arc
Lajos (1991), "A Bernoulli Excursion and Its Various Applications", Advances in Applied Probability, 23 (3), Applied Probability Trust: 557–585, doi:10.2307/1427622
Tournament_(graph_theory)
Reduction in pressure to lower than normal sea level atmospheric pressure
excursions from sea level to altitudes above 15,000 feet (4,600 m) without oxygen prebreathing may induce venous gas bubbles, with a 5% probability of
Hypobaric_decompression
Descending below the surface of the water to interact with the environment
dive sites without convenient shore entry may be provided by basic, day excursion, and live-aboard dive boats. Motivations to travel for scuba diving are
Underwater_diving
Change in the heritable characteristics of populations
161281098. PMC 55389. PMID 11470913. Felsenstein, Joseph (November 1979). "Excursions along the Interface between Disruptive and Stabilizing Selection". Genetics
Evolution
Early photographic technique
Duperly, a Frenchman, produced a booklet of Daguerreotypes, Daguerian Excursions in Jamaica, being a collection of views ... taken on the spot with the
Daguerreotype
Annual parade and dance in St. Louis, Missouri
(Missouri) Gazette said: "The interest in this affair is simply amazing. Excursion trains on all the railroads leading into the city have been crammed to
Veiled Prophet Parade and Ball
Veiled_Prophet_Parade_and_Ball
Representation of a type of random process
Vol. 131, p. 518–532. Theodoridis, Sergios (2015-04-10). "Chapter 1. Probability and Stochastic Processes". Machine Learning: A Bayesian and Optimization
Autoregressive_model
Strong explosion observed on stars
1051/0004-6361/201321080. S2CID 55137950. Jull, A.J.Timothy; et al. (25 April 2014). "Excursions in the 14C record at A.D. 774– 775 in tree rings from Russia and America"
Superflare
Restrictions imposed during the COVID-19 pandemic
Carvalho N, Bablani L, Wilson N, Stevenson M (28 September 2020). "The probability of the 6-week lockdown in Victoria (commencing 9 July 2020) achieving
COVID-19_lockdowns
English polymath (1642–1727)
Mathematica. pp. 142–146. Hykšová, Magdalena. GEOMETRIC PROBABILITY APPLICATIONS THROUGH HISTORICAL EXCURSION (PDF). ESU-6. Hykšová, Magdalena; Kalousová, Anna;
Isaac_Newton
In probability theory and statistics, a continuous-time stochastic process, or a continuous-space-time stochastic process is a stochastic process for
Continuous-time stochastic process
Continuous-time_stochastic_process
Role-playing video game
relationship level, as well as "outings" that involve sending two Miis on an excursion during inn visits to increase their relationship level. Outings are accessed
Miitopia
Type of role-playing games
sophistication from simple coin tosses to systems of random tables adjusting probabilities based on previous game states. Software implementations of oracle systems
Solo_role-playing_game
Branch of elementary mathematics
Courier Corporation. ISBN 978-0-486-31981-0. Kleiner, Israel (2012). Excursions in the History of Mathematics. Springer Science & Business Media. ISBN 978-0-8176-8268-2
Arithmetic
President of Mexico from 1876 to 1911
February 1864. Díaz's hold was consolidated enough that he began making excursions into Veracruz, and Minatitlán was taken by 28 March 1864. Meanwhile, French
Porfirio_Díaz
Time taken by a signal to change to a high value
either positive or negative step response, even if a displayed negative excursion is popularly termed fall time. Rise time is an analog parameter of fundamental
Rise_time
One of the two main New Zealand islands
network, was cancelled in 2002. It ran for a few days in 2025 as a tourist excursion, and in 2026 a similar tourist service named The Mainlander operated occasionally
South_Island
Rapid transit system serving the San Francisco Bay Area
entering and exiting at the same station within 30 minutes incurred an "excursion fare" of $6.40 – significantly higher than many station-to-station fares
Bay_Area_Rapid_Transit
1919 book by John Maynard Keynes
leading economist. As an academic, Keynes had worked on his Treatise on Probability, which includes a critique of conventional economic thinking under conditions
The Economic Consequences of the Peace
The_Economic_Consequences_of_the_Peace
Tabulated data to facilitate safe diving ascents
tables. 1% Risk tables are tables which satisfy the condition of a high probability (c0.95) of a low risk (c0.01) of producing symptomatic decompression
Decompression_tables
Strong surface-level winds that radiate from a single point
Airport (ALA)". aviation-safety.net. Retrieved 12 September 2022. "Runway excursion, USAir Inc., Flight 183, McDonnell Douglas DC9-31, N964VJ, Detroit Metropolitan
Downburst
Algorithm for computing greatest common divisors
integers. The probability of a given quotient q is approximately ln |u/(u − 1)| where u = (q + 1)2. For illustration, the probability of a quotient of
Euclidean_algorithm
"Absolute dating of the European Neolithic using the 5259 BC rapid 14C excursion", Nature Communications, 2024 doi:10.1038/s41467-024-48402-1 Höflmayer
Chronology of the ancient Near East
Chronology_of_the_ancient_Near_East
Underwater diving breathing gas supplied from the surface
equipment. A diver's umbilical supplied from a bell gas panel is called an excursion umbilical, and the supply from the surface to the bell panel is the bell
Surface-supplied_diving
Large minefield laid by the United States in World War I
temporarily marking the end point of a mining excursion to avoid leaving an un-mined gap when the next excursion started. These buoys were subject to potential
North_Sea_Mine_Barrage
Upper airway closure disrupting sleep
collapsibility while reducing the intrathoracic volume and diaphragm excursion. Moreover, excessive daytime sleepiness resulting from sleep fragmentation
Obstructive_sleep_apnea
U.S. government cryptographic standard
module's normal operating ranges for voltage and temperature. Intentional excursions beyond the normal operating ranges may be used by an attacker to thwart
FIPS_140-2
Galaxy in the constellation Andromeda
"NGC 404: A Rejuvenated Lenticular Galaxy on a Merger-induced, Blueward Excursion Into the Green Valley". The Astrophysical Journal Letters. 714 (1): L171–L175
NGC_404
Family of sets where every disjoint subfamily has k or fewer sets
Combinatorics: Set Systems, Hypergraphs, Families of Vectors, and Combinatorial Probability, Cambridge University Press, p. 82, ISBN 9780521337038. Duchet, Pierre
Helly_family
Equipment allowing or assisting the user to breathe in a hostile environment
user interface of the control and monitoring system can influence the probability of operator error. The endurance of a rebreather or life support system
Breathing_apparatus
travel, tourism, insurance
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travel, tourism, insurance