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Probabilistic concept
In mathematics, more specifically in stochastics, Doob's h-transform is a method to transform a Markov process into a new Markov process, which exhibits
Doob's_h-transform
Memoryless property of a stochastic process
an h {\displaystyle h} -transform–a method introduced by J.L. Doob to manipulate Markov processes. For a function h : S → ( 0 , ∞ ) {\displaystyle h:S\to
Markov_property
American mathematician (1910–2004)
(probability theory) Doob–Dynkin lemma Doob's h-transform Doob martingale Doob's martingale convergence theorems Doob's martingale inequality Doob–Meyer decomposition
Joseph_L._Doob
Discrete probability distribution
}(u)-2\,\nabla \log h(u,t),\\h(u,t)&=\sum _{i=1}^{n}w_{i}\,p_{t|0}(u\mid x_{i}),\end{aligned}}} reflecting a Doob's h-transformed for an SDE conditioned
Categorical_distribution
French mathematician
Princeton. In 2020, Carmona and François Delarue [fr] were awarded the Joseph L. Doob Prize by the American Mathematical Society for their two volume series Probabilistic
René_Carmona
Representation of a type of random process
function is the Fourier transform of the autocovariance function. In discrete terms this will be the discrete-time Fourier transform: Φ ( ω ) = 1 2 π ∑ n
Autoregressive_model
Method of statistical inference
( H ∣ E ) = P ( E ∣ H ) P ( H ) P ( E ) = P ( E ∣ H ) P ( H ) P ( E ∣ H ) P ( H ) + P ( E ∣ ¬ H ) P ( ¬ H ) = 1 1 + ( 1 P ( H ) − 1 ) P ( E ∣ ¬ H ) P
Bayesian_inference
distribution Box–Cox transformation – redirects to Power transform Box–Jenkins Box–Muller transform Box–Pierce test Box plot Branching process Bregman divergence
List_of_statistics_articles
Statistical concept
null hypothesis H 0 {\displaystyle H_{0}} is a set of distributions for data Y {\displaystyle Y} . An e-variable for H 0 {\displaystyle H_{0}} is a nonnegative
E-values
Polish-Canadian mathematician (born 1963)
2019. Zworski and Semyon Dyatlov are the recipients of the 2026 Joseph L. Doob prize, for their 2019 book Mathematical Theory of Scattering Resonances.
Maciej_Zworski
Random process independent of past history
t, Pr ( X ( t + h ) = j ∣ X ( t ) = i ) = δ i j + q i j h + o ( h ) , {\displaystyle \Pr(X(t+h)=j\mid X(t)=i)=\delta _{ij}+q_{ij}h+o(h),} where δ i j {\displaystyle
Markov_chain
Plot device in mythology and fiction
Penelope Reed Doob, The Idea of the Labyrinth: from Classical Antiquity through the Middle Ages, p 177, ISBN 0-8014-8000-0 Penelope Reed Doob, The Idea of
Quest
Stochastic process generalizing Brownian motion
values in ( H , B ( H ) ) {\displaystyle (H,{\mathcal {B}}(H))} is Gaussian if for all h ∈ H {\displaystyle h\in H} the projection ⟨ Z , h ⟩ {\displaystyle
Wiener_process
Indian singer and composer (born 1991)
2020. "Exclusive! Guru Randhawa: It was always my wish to workout and transform my body". The Times of India. 12 August 2020. Archived from the original
Guru_Randhawa
Concept within complex analysis
bounded linear operator H on Lp(T), when 1 < p < ∞ (up to a scalar multiple, it is the Hilbert transform on the unit circle), and H also maps L1(T) to weak-L1(T)
Hardy_space
Method in statistics
covariances of the transformed quantities. For example, the formulae presented in Klein (1953, p. 258) are: Var ( h r ) = ∑ i ( ∂ h r ∂ B i ) 2 Var
Delta_method
American-born French entertainer (1906–1975)
discussed and illustrated in rare footage in the 2005 Linda Atkinson/Nick Doob documentary, Carmen and Geoffrey. In 2011, Sonia Rolland portrayed Baker
Josephine_Baker
Fundamental theorem in probability theory and statistics
statement can be made about Fourier transforms, since the characteristic function is essentially a Fourier transform. Let Sn be the sum of n random variables
Central_limit_theorem
Elaborate, confusing structure in Greek mythology
Companion: A Guide to Walking the Labyrinth to Heal and Transform, Penguin Books, 2006, ISBN 1-59448-182-2. Doob, Penelope Reed (1992). The Idea of the Labyrinth:
Labyrinth
Stochastic process modeling random walk with friction
x 0 = 0 {\displaystyle x_{0}=0} can be represented as a scaled, time-transformed Wiener process: x t = σ 2 θ e − θ t W e 2 θ t − 1 {\displaystyle x_{t}={\frac
Ornstein–Uhlenbeck_process
American mathematician (1858–1928)
delegated the preceptor appointments to Fine, giving him the opportunity to transform Princeton's programs in those fields. Fine had an extraordinary ability
Henry_Burchard_Fine
Interpretation of quantum mechanics
obtained by the first order Legendre transform: H ∘ ( x , p ∘ , t ) = p ∘ , i v ∘ i − L ( x , v ∘ , t ) . {\displaystyle H_{\circ }(x,p_{\circ },t)=p_{\circ
Stochastic_quantum_mechanics
{\displaystyle v_{n}(x)=u_{n}(t)} , t = F ( x ) {\displaystyle t=F(x)} transforms to the so-called uniform empirical process u n {\displaystyle u_{n}}
Khmaladze_transformation
Economic theory that asset prices fully reflect all available information
(2019). Curable: How an Unlikely Group of Radical Innovators Is Trying to Transform Our Health Care System. Chelsea Green Publishing, ISBN 1603589279, p.
Efficient-market_hypothesis
Hungarian and American mathematician and physicist (1903–1957)
the conference, von Neumann suggested to Gödel that he should try to transform his results for undecidable propositions about integers. Less than a month
John_von_Neumann
Graph of chess rook moves
ISBN 9780691130620 Murray, H. J. R. (January 1902), "The knight's tour: ancient and oriental", The British Chess Magazine, vol. 22, no. 1, pp. 1–7 Doob, Michael (1970)
Rook's_graph
(integral transform) Mellin inversion theorem (complex analysis) Stahl's theorem (matrix analysis) Titchmarsh theorem (integral transform) Fredholm's
List_of_theorems
Punctuation and accent mark (~, ◌̃)
informally, as "eff twiddle". This can be used to denote the Fourier transform of f, or a lift of f, and can have a variety of other meanings depending
Tilde
American mathematician (1919–1985)
number of parameters and in any number of unknowns, one can effectively transform this equation into another with the same parameters but in only N unknowns
Julia_Robinson
contribution of (Ahlswede & Winter 2003) was the extension of the Laplace-transform method used to prove the scalar Chernoff bound (see Chernoff bound#Additive
Matrix_Chernoff_bound
Personal sense of one's own gender
and hatred for the parent ascribed the same gender, and this hatred transformed into (unconscious) transference and (conscious) identification with the
Gender_identity
distribution / (1:D) (a,b,0) class of distributions / (1:D) Anscombe transform Bernoulli distribution / (1:B) Beta distribution / (1:C) Bose–Einstein
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Annual session of lectures
replaced by Norbert Wiener (Massachusetts Institute of Technology): Fourier transforms in the complex domain. 1935 Harry Vandiver (University of Texas): Fermat's
Colloquium_Lectures_(AMS)
Canadian statistician
the Bayesian method is consistent in agreement with earlier findings of Doob (1948). Freedman was the author or co-author of 200 articles, 20 technical
David_A._Freedman
Distribution of variables which satisfies a stability property under linear combinations
{\displaystyle f} is the Fourier transform of f . {\displaystyle f.} The density function is then the inverse Fourier transform of the characteristic function:
Stable_distribution
Canada: A Reader's Guide, (2nd ed., 2000) by J.André Senécal, online. James H. Marsh (1999). The Canadian Encyclopedia. The Canadian Encyclopedia. ISBN 978-0-7710-2099-5
Bibliography_of_Canada
awarded the Salem Prize for solving conjectures about the Bilinear Hilbert Transform Richard Leibler, Ph.D. 1939 – mathematician and cryptanalyst; formulated
List of University of Illinois Urbana-Champaign people
List_of_University_of_Illinois_Urbana-Champaign_people
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DOOBS H-TRANSFORM
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