The DOI matches its Crossref record.
Probability and Random Processes.
Abstract
Abstract This third edition of this successful text gives a rigorous and extensive introduction to probability theory and an account in some depth of the most important random processes. It includes various topics which are suitable for undergraduate courses, but are not routinely taught. It is suitable for students of probability at all levels. There are four main aims: 1) to provide a thorough but straightforward account of basic probability, giving the reader a natural feel for the subject unburdened by oppressive technicalities, 2) to discuss important random processes in depth with many examples. 3) to cover a range of important but less routine topics, 4) to impart to the beginner the flavour of more advanced work. The book begins with basic ideas common to many undergraduate courses in mathematics, statistics and the sciences; it concludes with topics usually found at graduate level. The ordering and numbering of material in this third edition has been mostly preserved from the second. Minor alterations and additions have been added for clearer exposition. Highlights include new sections on sampling and Markov chain Monte Carlo, geometric probability, coupling and Poisson approximation, large deviations, spatial Poisson processes, renewal-reward, queuing networks, stochastic calculus, Itô's formula and option pricing in the Black- Scholes model for financial markets. In addition there are many (nearly 400) new exercises and problems that are entertaining and instructive; their solutions can be found in the companion volume 'One Thousand Exercises in Probability', (OUP).
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“An important theorem from probability theory (see, e.g., p. 232 in [39]) states that if is irreducible (i.e., any state in can be reached from any other state in in finitely many steps with probability ) and aperiodic (i.e., its state transitions cannot be trapped in deterministic cycles), then the probability converges for to a probability that does not depend on the initial state .”
From Neural dynamics as sampling: a model for stochastic computation in recurrent networks of spiking neurons (2011) · cites this paper as [39]
Citations
Cited by
Sorted by citations
Items 101–200 of 1,001
Optimal Design of Sequential Real-Time Communication Systems
Mahajan, A., & Teneketzis, D. (2009) · IEEE Transactions on Information Theory · doi:10.1109/tit.2009.2030462 · Cited by 87
Freely Jointed Polymers Made of Droplets
McMullen, A., Holmes-Cerfon, M. C., Sciortino, F., et al. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.138002 · Cited by 90
Monte Carlo Non-Local Means: Random Sampling for Large-Scale Image Filtering
Chan, S. H., Zickler, T. E., & Lu, Y. (2014) · IEEE Transactions on Image Processing · doi:10.1109/tip.2014.2327813 · Cited by 89
The weakness of strong ties: Sampling bias, social ties, and nepotism in family business succession
Liu, C., Eubanks, D. L., & Nick Chater, A. (2015) · The Leadership Quarterly · doi:10.1016/j.leaqua.2015.02.007 · Cited by 90
Fractional-order modeling of neutron transport in a nuclear reactor
Vyawahare, V. A., & Nataraj, P. S. V. (2013) · Applied Mathematical Modelling · doi:10.1016/j.apm.2013.05.023 · Cited by 89
Optimal Configuration of 802.11e EDCA for Real-Time and Data Traffic
Serrano, P., Banchs, A., Patras, P., et al. (2010) · IEEE Transactions on Vehicular Technology · doi:10.1109/tvt.2010.2043274 · Cited by 89
High-Frequency Replanning Under Uncertainty Using Parallel Sampling-Based Motion Planning
Sun, W. Y., Patil, S., & Alterovitz, R. (2015) · IEEE Transactions on Robotics · doi:10.1109/tro.2014.2380273 · Cited by 87
Energy-Efficient Control Strategies for Machine Tools With Stochastic Arrivals
Frigerio, N., & Matta, A. (2014) · IEEE Transactions on Automation Science and Engineering · doi:10.1109/tase.2014.2344507 · Cited by 87
Spectrum Sensing Using a Hidden Bivariate Markov Model
Nguyen, T. T., Mark, B. L., & Ephraim, Y. (2013) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2013.072513.121864 · Cited by 86
Classical and quantum probability
Streater, R. F. (2000) · Journal of Mathematical Physics · doi:10.1063/1.533322 · Cited by 90
Mesoscale Simulation of Asphaltene Aggregation
Wang, J., & Ferguson, A. L. (2016) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.6b05925 · Cited by 83
CHAOTIC DISINTEGRATION OF THE INNER SOLAR SYSTEM
Batygin, K., Morbidelli, A., & Holman, M. J. (2015) · The Astrophysical Journal · doi:10.1088/0004-637x/799/2/120 · Cited by 92
Delay and Peak-Age Violation Probability in Short-Packet Transmissions
Devassy, R., Durisi, G., Ferrante, G. C., et al. (2018) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2018.8437671 · Cited by 84
Pilot-Based LMMSE Channel Estimation for OFDM Systems With Power–Delay Profile Approximation
Hung, K.-C., & Lin, D. W. (2009) · IEEE Transactions on Vehicular Technology · doi:10.1109/tvt.2009.2029862 · Cited by 83
Sampling-Based Optimal Control Synthesis for Multirobot Systems Under Global Temporal Tasks
Kantaros, Y., & Zavlanos, M. M. (2018) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2018.2853558 · Cited by 82
Models and Algorithms for Tracking of Maneuvering Objects Using Variable Rate Particle Filters
Godsill, S. J., Vermaak, J., Ng, W., & Li, J. F. (2007) · Proceedings of the IEEE · doi:10.1109/jproc.2007.894708 · Cited by 81
Approximation Algorithms for Reliable Stochastic Combinatorial Optimization
Nikolova, E. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-15369-3_26 · Cited by 81
Capacity of a Nonlinear Optical Channel With Finite Memory
Agrell, E., Alvarado, A., Durisi, G., et al. (2014) · Journal of Lightwave Technology · doi:10.1109/jlt.2014.2328518 · Cited by 80
Introduction and snapshot review: Relating infectious disease transmission models to data
O’Neill, P. D. (2010) · Statistics in Medicine · doi:10.1002/sim.3968 · Cited by 81
Brownian Motion in Planetary Migration
Murray‐Clay, R. A., & Chiang, E. I. (2006) · The Astrophysical Journal · doi:10.1086/507514 · Cited by 89
Why Does the Kronecker Model Result in Misleading Capacity Estimates?
Raghavan, V., Kotecha, J. H., & Sayeed, A. M. (2010) · IEEE Transactions on Information Theory · doi:10.1109/tit.2010.2059811 · Cited by 78
Average case and smoothed competitive analysis of the multi-level feedback algorithm
Becchetti, L., Leonardi, S., Marchetti-Spaccamela, A., et al. (2004) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.2003.1238219 · Cited by 77
Information Theoretic Foundations of Adaptive Coded Modulation
Caire, G., & Kumar, K. R. (2007) · Proceedings of the IEEE · doi:10.1109/jproc.2007.904444 · Cited by 77
A Mathematical Analysis of the Generation and Termination of Calcium Sparks
Hinch, R. (2004) · Biophysical Journal · doi:10.1016/s0006-3495(04)74203-4 · Cited by 76
Kordijazi, A., Zhao, T. Q., Zhang, J., Alrfou, K., & Rohatgi, P. K. (2021) · JOM · doi:10.1007/s11837-021-04701-2 · Cited by 77
Machine Learning for First-Order Theorem Proving
Bridge, J. P., Holden, S. B., & Paulson, L. C. (2014) · Journal of Automated Reasoning · doi:10.1007/s10817-014-9301-5 · Cited by 76
Enabling Ultrareliable and Low-Latency Communications Under Shadow Fading by Massive MU-MIMO
Zeng, J. J., Lv, T., Liu, R. P., Su, X., Guo, Y. J., & Beaulieu, N. C. (2019) · IEEE Internet of Things Journal · doi:10.1109/jiot.2019.2945106 · Cited by 71
Honarmandi, P., & Arróyave, R. (2020) · Integrating materials and manufacturing innovation · doi:10.1007/s40192-020-00168-2 · Cited by 72
On pth roots of stochastic matrices
Higham, N. J., & Lijing Lin, A. (2010) · Linear Algebra and its Applications · doi:10.1016/j.laa.2010.04.007 · Cited by 74
Agreement in presence of noise: pseudogradients on random geometric networks
Hatano, Y., Das, A. K., & Mesbahi, M. (2006) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.2005.1583185 · Cited by 72
Abstract representations of events arise from mental errors in learning and memory
Lynn, C. W., Kahn, A. E., Nyema, N., & Bassett, D. S. (2020) · Nature Communications · doi:10.1038/s41467-020-15146-7 · Cited by 65
Renewal theory-based life-cycle analysis of deteriorating engineering systems
Kumar, R., & Gardoni, P. (2014) · Structural Safety · doi:10.1016/j.strusafe.2014.03.012 · Cited by 71
CHAOTIC DISINTEGRATION OF THE INNER SOLAR SYSTEM
Batygin, K., Morbidelli, A., & Holman, M. J. (2015) · Cited by 71
Woolley, T. E., Baker, R. E., Gaffney, E. A., & Maini, P. K. (2011) · Physical Review E · doi:10.1103/physreve.84.046216 · Cited by 68
Domínguez-García, A. D., Kassakian, J. G., Schindall, J. E., et al. (2008) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2008.01.007 · Cited by 69
Tseng, Y. Y., & Liang, J. (2005) · Molecular Biology and Evolution · doi:10.1093/molbev/msj048 · Cited by 67
Sequential Ensemble Learning for Outlier Detection: A Bias-Variance Perspective
Rayana, S., Zhong, W., & Akoglu, L. (2016) · Proceedings · doi:10.1109/icdm.2016.0154 · Cited by 74
Jiang, X.-T., Wang, Q., & Li, R. (2018) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2018.07.160 · Cited by 67
Low-Complexity Statistically Robust Precoder/Detector Computation for Massive MIMO Systems
Boroujerdi, M. N., Haghighatshoar, S., & Caire, G. (2018) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2018.2860951 · Cited by 67
Asymptotics of Implied Volatility far from Maturity
Tehranchi, M. R. (2009) · Journal of Applied Probability · doi:10.1239/jap/1253279843 · Cited by 67
Statistical reconstruction of two-phase random media
Feng, J., Li, C., Cen, S., & Owen, D. R. J. (2013) · Computers & Structures · doi:10.1016/j.compstruc.2013.03.019 · Cited by 69
Integrating stochasticity and network structure into an epidemic model
Dangerfield, C. E., Ross, J. V., & Keeling, M. J. (2008) · Journal of The Royal Society Interface · doi:10.1098/rsif.2008.0410 · Cited by 63
Arratia, R., Goldstein, L. J., & Kochman, F. (2019) · Probability Surveys · doi:10.1214/13-ps221 · Cited by 66
Performance of Cloud Centers with High Degree of Virtualization under Batch Task Arrivals
Khazaei, H., Mišić, J., & Mišić, V. B. (2013) · IEEE Transactions on Parallel and Distributed Systems · doi:10.1109/tpds.2012.318 · Cited by 65
ALTERNATIVE LOGICS AND APPLIED MATHEMATICS
Williamson, T. L. (2018) · Philosophical Issues · doi:10.1111/phis.12131 · Cited by 64
Random Walks on Truncated Cubes and Sampling 0-1 Knapsack Solutions
Morris, B., & Sinclair, A. (2004) · SIAM Journal on Computing · doi:10.1137/s0097539702411915 · Cited by 64
PET: Probabilistic Estimating Tree for Large-Scale RFID Estimation
Zheng, Y., & Li, M. (2011) · IEEE Transactions on Mobile Computing · doi:10.1109/tmc.2011.238 · Cited by 64
Mumenthaler, S. M., Foo, J., Leder, K., Choi, N. C., Agus, D. B., Pao, W. J., Mallick, P., & Michor, F. (2011) · Molecular Pharmaceutics · doi:10.1021/mp200270v · Cited by 61
On the number of independent cultural traits carried by individuals and populations
Lehmann, L., Aoki, K., & Feldman, M. W. (2011) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2010.0313 · Cited by 64
Quadrature Spatial Modulation for 5G Outdoor Millimeter–Wave Communications: Capacity Analysis
Younis, A., Abuzgaia, N., Mesleh, R., et al. (2017) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2017.2670545 · Cited by 63
Random Multipolar Driving: Tunably Slow Heating through Spectral Engineering
Zhao, H., Mintert, F., Moessner, R., et al. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.040601 · Cited by 63
The Network Origins of Large Economic Downturns
Acemoğlu, D., Ozdaglar, A., & Tahbaz-Salehi, A. (2013) · National Bureau of Economic Research · doi:10.3386/w19230 · Cited by 63
Leader–follower containment control over directed random graphs
Kan, Z., Shea, J. M., & Dixon, W. E. (2016) · Automatica · doi:10.1016/j.automatica.2015.12.016 · Cited by 62
Strategic Safety Stocks in Supply Chains with Evolving Forecasts
Schoenmeyr, T., & Graves, S. C. (2009) · Manufacturing & Service Operations Management · doi:10.1287/msom.1080.0245 · Cited by 62
The Potential of Moving Relays - A Performance Analysis
Sui, Y., Papadogiannis, A., & Svensson, T. (2012) · IEEE Vehicular Technology Conference · doi:10.1109/vetecs.2012.6240247 · Cited by 61
Wang, L., Ravichandran, N., & Juang, C. H. (2012) · Computers and Geotechnics · doi:10.1016/j.compgeo.2012.03.003 · Cited by 61
Computation and Simulation of Evolutionary Game Dynamics in Finite Populations
Hindersin, L., Wu, B., Traulsen, A., & García, J. (2019) · Scientific Reports · doi:10.1038/s41598-019-43102-z · Cited by 57
Quantitative Analysis of Dynamic Fault Trees Based on the Structure Function
Merle, G., Roussel, J. ‐., & Lesage, J.-J. (2013) · Quality and Reliability Engineering International · doi:10.1002/qre.1487 · Cited by 60
On Mixing and Edge Expansion Properties in Randomized Broadcasting
Sauerwald, T. (2008) · Algorithmica · doi:10.1007/s00453-008-9245-4 · Cited by 60
Inhomogeneous Markov Models for Describing Driving Patterns
Iversen, E. B., Møller, J. K., Morales, J. M., & Madsen, H. (2016) · IEEE Transactions on Smart Grid · doi:10.1109/tsg.2016.2520661 · Cited by 60
Legenstein, R. A., & Maass, W. (2014) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1003859 · Cited by 55
A Practical Guide to Estimating the Heritability of Pathogen Traits
Mitov, V., & Stadler, T. (2017) · Molecular Biology and Evolution · doi:10.1093/molbev/msx328 · Cited by 58
Random Walk in Markovian EnvironmentPreprint
Dolgopyat, D., Keller, G., & Liverani, C. (2012) · Cited by 59
A model for the impact of contaminants on fish population dynamics
Huang, Q., Parshotam, L., Wang, H., et al. (2013) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2013.05.018 · Cited by 58
Chen, S., & Insley, M. C. (2011) · Journal of Economic Dynamics and Control · doi:10.1016/j.jedc.2011.08.010 · Cited by 58
Quasi-static rheology of foams. Part 2. Continuous shear flow
Kabla, A., Scheibert, J., & Debrégeas, G. (2007) · Journal of Fluid Mechanics · doi:10.1017/s0022112007007276 · Cited by 58
Mitchell, J. S., & Rabosky, D. L. (2016) · Methods in Ecology and Evolution · doi:10.1111/2041-210x.12626 · Cited by 58
Dong, Y., Wang, J., Shim, B., & Kim, D. I. (2016) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2016.2621378 · Cited by 58
Rapid Assessment of Wave and Surge Risk during Landfalling Hurricanes: Probabilistic Approach
Taflanidis, A. A., Kennedy, A. B., Westerink, J. J., et al. (2012) · Journal of Waterway Port Coastal and Ocean Engineering · doi:10.1061/(asce)ww.1943-5460.0000178 · Cited by 57
Stochastic von Bertalanffy models, with applications to fish recruitment
Lv, Q., & Pitchford, J. W. (2006) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2006.09.009 · Cited by 56
The design of multicentre trials
Fedorov, V. V., & Jones, B. C. (2005) · Statistical Methods in Medical Research · doi:10.1191/0962280205sm399oa · Cited by 56
Parameter estimation and remaining useful life prediction of lubricating oil with HMM
Du, Y., Wu, T., & Makiš, V. (2017) · Wear · doi:10.1016/j.wear.2016.11.047 · Cited by 55
A learning-theory approach to sensor networks
Simić, S. N. (2003) · IEEE Pervasive Computing · doi:10.1109/mprv.2003.1251168 · Cited by 55
Towards Behaviometric Security Systems: Learning to Identify a Typist
Nisenson, M., Yariv, I., El‐Yaniv, R., et al. (2003) · Lecture notes in computer science · doi:10.1007/978-3-540-39804-2_33 · Cited by 54
The Irish Sea cod recovery plan: some lessons learned
Kelly, C. J., Codling, E. A., & Rogan, E. (2006) · ICES Journal of Marine Science · doi:10.1016/j.icesjms.2005.12.001 · Cited by 55
Shape-based peak identification for ChIP-Seq
Hower, V., Evans, S. N., & Pachter, L. S. (2011) · BMC Bioinformatics · doi:10.1186/1471-2105-12-15 · Cited by 54
Minimum Energy Transmission Over a Wireless Channel With Deadline and Power Constraints
Zafer, M. A., & Modiano, E. (2009) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2009.2034202 · Cited by 54
Iterative Truncated Arithmetic Mean Filter and Its Properties
Jiang, X. (2011) · IEEE Transactions on Image Processing · doi:10.1109/tip.2011.2172805 · Cited by 54
Chapman, A. C., Rogers, A., Jennings, N. R., & Leslie, D. S. (2011) · The Knowledge Engineering Review · doi:10.1017/s0269888911000178 · Cited by 54
Harper, A. J. (2020) · Forum of Mathematics Pi · doi:10.1017/fmp.2019.7 · Cited by 54
Perfect state transfer in Laplacian quantum walk
Alvir, R., Dever, S., Lovitz, B., Myer, J., Tamon, C., Xu, Y., & Zhan, H. (2015) · Journal of Algebraic Combinatorics · doi:10.1007/s10801-015-0642-x · Cited by 52
Model and data limitations: the sources and implications of epistemic uncertainty
Rougier, J., & Beven, K. J. (2013) · Cambridge University Press eBooks · doi:10.1017/cbo9781139047562.004 · Cited by 56
A multinomial probit model of stochastic evolution
Myatt, D. P., & Wallace, C. (2003) · Journal of Economic Theory · doi:10.1016/s0022-0531(03)00069-3 · Cited by 51
Probabilistic anomaly detection in distributed computer networks
Burgess, M. (2005) · Science of Computer Programming · doi:10.1016/j.scico.2005.06.001 · Cited by 53
Asymptotically exact analysis of stochastic metapopulation dynamics with explicit spatial structure
Ovaskainen, O., & Cornell, S. J. (2005) · Theoretical Population Biology · doi:10.1016/j.tpb.2005.05.005 · Cited by 50
Covariation Is a Poor Measure of Molecular Coevolution
Talavera, D., Lovell, S. C., & Whelan, S. (2015) · Molecular Biology and Evolution · doi:10.1093/molbev/msv109 · Cited by 54
Power Control and Channel Allocation for D2D Underlaid Cellular Networks
Abdallah, A., Mansour, M. M., & Chehab, A. (2018) · IEEE Transactions on Communications · doi:10.1109/tcomm.2018.2812731 · Cited by 53
Cell-Free Massive MIMO for URLLC: A Finite-Blocklength Analysis
Lancho, A., Durisi, G., & Sanguinetti, L. (2023) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2023.3265303 · Cited by 53
Environmental complexity favors the evolution of learning
Dridi, S., & Lehmann, L. (2015) · Behavioral Ecology · doi:10.1093/beheco/arv184 · Cited by 55
Asymptotically Optimal Planning for Non-Myopic Multi-Robot Information Gathering
Kantaros, Y., Schlotfeldt, B., Atanasov, N., et al. (2019) · doi:10.15607/rss.2019.xv.062 · Cited by 51
Wang, D., Jiao, F., & Mao, X. (2019) · International Journal of Mechanical Sciences · doi:10.1016/j.ijmecsci.2019.105336 · Cited by 51
Ye, K., Tang, X. J., Zheng, Y., et al. (2021) · Process Safety and Environmental Protection · doi:10.1016/j.psep.2021.01.030 · Cited by 51
Almost sure convergence to consensus in Markovian random graphs
Matei, I., Martins, N. C., & Baras, J. S. (2008) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.2008.4738888 · Cited by 50
Epistasis and the Dynamics of Reversion in Molecular Evolution
McCandlish, D. M., Shah, P., & Plotkin, J. B. (2016) · Genetics · doi:10.1534/genetics.116.188961 · Cited by 52
Bridges of Bluetooth county: topologies, scheduling, and performance
Misic, J., & Mišić, V. B. (2003) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2002.807340 · Cited by 51
Perception-Based Temporal Logic Planning in Uncertain Semantic Maps
Kantaros, Y., Kalluraya, S., Jin, Q., et al. (2022) · IEEE Transactions on Robotics · doi:10.1109/tro.2022.3144073 · Cited by 49
Lin, J., & Zhang, F. (2024) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2024.3456473 · Cited by 71
A two-step matrix splitting iteration for computing PageRank
Gu, C., Xie, F., & Zhang, K. (2014) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2014.09.022 · Cited by 49
A Profust Reliability Based Approach to Prognostics and Health Management
Zhao, Z., Quan, Q., & Cai, K. (2014) · IEEE Transactions on Reliability · doi:10.1109/tr.2014.2299111 · Cited by 49
Joint Routing and Resource Allocation for Delay Minimization in Cognitive Radio Based Mesh Networks
El-Sherif, A. A., & Mohamed, A. M. S. (2014) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2013.112513.122082 · Cited by 49
Metadata
- Authors
- Grimmett, G. R., & Stirzaker, D. R.
- ORCID
- Grimmett, Geoffrey R
- Publisher
- Oxford University PressOxford
- Published
- 2001-05-31
- OpenAlex
- W4388297583
- Cited by
- 1,850
- References
- 0
- Citations by year
- 2026: 32 · 2025: 43 · 2024: 77 · 2023: 71 · 2022: 93 · 2021: 95 · 2020: 90 · 2019: 128 · 2018: 137 · 2017: 87 · 2016: 87 · 2015: 113 · 2014: 106 · 2013: 105 · 2012: 108
- FWCI
- 5.56
- Type
- book
- Language
- en
- Open access
- closed
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
- Physical Sciences › Mathematics › Applied Mathematics › Point processes and geometric inequalities
- Keywords
- probability theory, stochastic processes, Markov chain Monte Carlo, geometric probability, coupling, Poisson approximation, large deviations, spatial Poisson process, queueing networks, stochastic calculus, Itô formula, option pricing, Black-Scholes model, sampling
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
