A) A process that only occurs in discrete steps. B) A process that remains constant over time. C) A random process evolving over time. D) A deterministic process with fixed outcomes.
A) Maximum value the process can attain. B) Average value of the process over time. C) Set of all possible values that the process can take. D) Exact value of the process at a given time.
A) Bernoulli distribution B) Normal distribution C) Uniform distribution D) Exponential distribution
A) Short-term analysis is sufficient for understanding long-term behavior. B) Behavior is completely random. C) Long-term average behavior can be inferred from a single realization. D) No inference can be made about long-term behavior.
A) Measure of correlation between values at different time points. B) Average of the process over time. C) Maximum correlation possible for the process. D) Exact form of the process at a given time.
A) Brownian motion B) Geometric process C) Markov process D) Deterministic process
A) Determines the initial state of the process. B) Calculates the average time spent in each state. C) Describes probabilities of moving to different states. D) Specifies the final state of the process.
A) As the number of observations increases, sample averages converge to expected values. B) Expected values change with the number of observations. C) Sample averages diverge from expected values. D) Randomness decreases with more observations.
A) Only in finance and economics. B) Biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, and telecommunications. C) Primarily in linguistics and anthropology. D) Exclusively in mathematics and statistics.
A) Louis Bachelier. B) Andrey Kolmogorov. C) Albert Einstein. D) A. K. Erlang.
A) It can only take integer values. B) The state space is the real line. C) The state space is finite. D) The index set consists of integers.
A) 1713 B) 1888 C) 1662 D) 1934
A) Ladislaus Bortkiewicz B) Jakob Bernoulli C) Joseph Doob D) Aleksandr Khinchin
A) Andrei Kolmogorov B) Aleksandr Khinchin C) Joseph Doob D) Francis Edgeworth
A) 17th century B) 18th century C) 14th century D) 16th century
A) Andrei Kolmogorov B) Ladislaus Bortkiewicz C) Jakob Bernoulli D) Aleksandr Khinchin
A) Ars Conjectandi B) Principia Mathematica C) Philosophiæ Naturalis Principia Mathematica D) De Motu Corporum
A) Latin word meaning 'chance' B) Middle French word meaning 'speed, haste' C) Greek word meaning 'to aim at a mark' D) Old English word meaning 'luck'
A) 1713 B) 1662 C) 1934 D) 1888
A) Joseph Doob B) Andrei Kolmogorov C) Jakob Bernoulli D) Ladislaus Bortkiewicz
A) {X(t)}_{t∈T} B) X(t) C) {X_t}_{t∉T} D) {X_t}
A) {X(t)}_{t∈T} B) X(t) C) {X_t} D) {X_t}_{t∈T}
A) 1-p B) 0.5 C) p D) t
A) A continuous distribution B) An idealized coin flip C) A Poisson event D) A deterministic outcome
A) 1-p B) p C) 0.5 D) t
A) (−∞, ∞) B) [0, ∞) C) {0, 1, 2, ...} D) [1, ∞)
A) Drawing cards from a deck B) Measuring time intervals C) Repeatedly flipping a coin D) Rolling a die
A) Zero B) One C) p D) t
A) 0 or 1 B) -1 or 0 C) +1 or -1 D) Any real number
A) Rational numbers B) Natural numbers C) Real numbers D) The integers
A) The natural numbers B) Complex numbers C) Real numbers D) Integers
A) Albert Einstein B) Andrey Kolmogorov C) Kiyoshi Itô D) Norbert Wiener
A) Lévy flight B) Poisson process C) Markov chain D) Brownian motion
A) 1-dimensional B) 3-dimensional C) n-dimensional D) 2-dimensional
A) Electromagnetism B) Quantitative finance C) Classical mechanics D) Thermodynamics
A) Efficient market hypothesis B) CAPM model C) Modern portfolio theory D) Black–Scholes–Merton model
A) t1 and t2 are independent. B) t1 > t2. C) t1 = t2. D) t1 ≤ t2.
A) Probability measure. B) Function composition. C) Set intersection. D) Union of sets.
A) The second moment. B) The index set. C) The mean and variance. D) Finite-dimensional distributions.
A) No specific order. B) A partial order relation. C) A total order relation. D) An unordered set.
A) Stationarity B) Continuity C) Independence D) Markov property
A) 1907 B) 1928 C) 1912 D) 1931
A) Albert Einstein B) Norbert Wiener C) Thorvald Thiele D) Louis Bachelier
A) Constant amplitude discrete linear graph. B) Cumulative distribution function. C) Continue à droite, limite à gauche (right-continuous with left limits). D) Continuous and differentiable at all points.
A) 1900s B) 1920s C) 1950s D) 1960s
A) Fourier equation B) Diffusion equation C) Least squares equation D) Differential equation
A) V B) R C) C D) E
A) Harald Cramér B) Wolfgang Doeblin C) Paul Lévy D) Andrei Kolmogorov
A) Louis Bachelier B) Percy Daniell C) Albert Einstein D) Marian Smoluchowski
A) 1920 B) 1909 C) 1903 D) 1910
A) Émile Borel B) Paul Lévy C) Sergei Bernstein D) Andrei Kolmogorov
A) Equivalent B) Modification C) Version D) Stochastic equivalence
A) Maurice Fréchet B) Sydney Chapman C) Poincaré D) Andrey Kolmogorov
A) David Hilbert B) Henri Lebesgue C) Andrei Kolmogorov D) Paul Lévy
A) Norbert Wiener B) Andrey Kolmogorov C) Sydney Chapman D) Louis Bachelier
A) Louis Bachelier B) Norbert Wiener C) Thorvald Thiele D) Albert Einstein
A) Martin Hairer B) Srinivasa Varadhan C) Wendelin Werner D) Gilbert Hunt
A) An index set for time. B) A sigma-algebra on Ω. C) A probability measure. D) A random variable.
A) Émile Borel B) Henri Lebesgue C) Sergei Bernstein D) Paul Lévy
A) A dense countable subset. B) An uncountable number of elements. C) A finite number of elements. D) No specific properties.
A) 1970 B) 1953 C) 1945 D) 1960
A) Maurice Fréchet B) Poincaré C) Eugene Dynkin D) Andrey Kolmogorov
A) Gilbert Hunt B) Shizuo Kakutani C) Kiyosi Itô D) Paul-André Meyer
A) Anatoliy Skorokhod B) Norbert Wiener C) Paul Lévy D) Andrey Kolmogorov
A) C B) F C) D D) S
A) Josiah Gibbs B) James Clerk Maxwell C) Rudolf Clausius D) Ludwig Boltzmann
A) Louis Bachelier B) William Feller C) Paul Ehrenfest D) Sydney Chapman
A) A.K. Erlang B) Filip Lundberg C) Harry Bateman D) Siméon Poisson
A) Albert Einstein B) Marian Smoluchowski C) Percy Daniell D) Jean Perrin
A) 1912 B) 1880 C) 1900 D) 1950s
A) Kiyosi Itô B) Gilbert Hunt C) Joseph Doob D) Alexander Wentzell
A) The Theory of Stochastic Processes B) Foundations of Probability Theory C) Grundbegriffe der Wahrscheinlichkeitsrechnung D) Introduction to Measure Theory
A) Non-linear models B) Stochastic models C) Deterministic models D) Linear models
A) Rudolf Clausius B) Josiah Gibbs C) Ludwig Boltzmann D) James Clerk Maxwell
A) Srinivasa Varadhan B) Alexander Wentzell C) Gilbert Hunt D) Paul-André Meyer
A) Phone calls B) Differential equations C) Alpha particles D) Insurance claims
A) Maurice Fréchet B) Sydney Chapman C) Irénée-Jules Bienaymé D) Andrey Markov
A) Jean Ville B) Gilbert Hunt C) Kiyosi Itô D) Joseph Doob
A) Normality and stationarity B) Consistency conditions C) Independence and identical distribution D) Linearity and continuity
A) Sergei Bernstein B) Gilbert Hunt C) Joseph Doob D) Shizuo Kakutani
A) Theory of large deviations B) Stochastic calculus C) Schramm–Loewner evolution D) Potential theory
A) 1932 B) 1937 C) 1934 D) 1928
A) Point process B) Gambler's ruin C) Renewal process D) Brownian motion
A) A gambling problem. B) The invention of algebra. C) The study of geometry. D) The development of calculus.
A) They require a dense countable subset of their index set to be separable. B) They cannot be separable. C) They are always separable. D) Their separability depends on the state space S.
A) 1929 B) 1945 C) 1933 D) 1925
A) Jacob Bernoulli B) Christiaan Huygens C) George Pólya D) Karl Pearson
A) Joseph Doob B) Andrei Kolmogorov C) Harald Cramér D) William Feller
A) Percy Daniell B) Thorvald Thiele C) Jean Perrin D) Leonard Savage
A) Physics B) Measure theory C) Financial mathematics D) Time-series analysis
A) Orthogonality implies independence. B) Uncorrelatedness implies independence. C) They are unrelated concepts. D) Independence implies uncorrelatedness.
A) Marian Smoluchowski B) Leonard Savage C) Louis Bachelier D) Norbert Wiener
A) 1905 B) 1930s C) 1713 D) 1919
A) Joseph Doob B) Kiyosi Itô C) Gilbert Hunt D) Sergei Bernstein
A) Andrey Kolmogorov B) Norbert Wiener C) Joseph Doob D) Paul Lévy
A) Simulating non-random objects B) Markov chain Monte Carlo methods in Bayesian statistics C) Analyzing linear regression models D) Solving deterministic differential equations
A) The Russian Revolution B) World War II C) The Great Depression D) The Cold War
A) Statistical mechanics B) Classical mechanics C) Thermodynamics D) Quantum mechanics
A) Itô's lemma B) Central Limit Theorem C) Kolmogorov's existence theorem D) Lévy's continuity theorem
A) 1912 B) 1906 C) 1928 D) 1931 |