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1. Stochastic processes and boundary value problems: In mathematics, some boundary value problems can be solved using the methods of stochastic analysis. Perhaps the most celebrated example is Shizuo Kakutani's 1944 solution of the Dirichlet problem for the Laplace operator using Brownian motion. [100%] 2023-09-29 [Partial differential equations] [Stochastic differential equations]...
2. Stochastic processes and boundary value problems: In mathematics, some boundary value problems can be solved using the methods of stochastic analysis. Perhaps the most celebrated example is Shizuo Kakutani's 1944 solution of the Dirichlet problem for the Laplace operator using Brownian motion. [100%] 2025-04-24 [Boundary value problems] [Partial differential equations]...
3. Law (stochastic processes): In mathematics, the law of a stochastic process is the measure that the process induces on the collection of functions from the index set into the state space. The law encodes a lot of information about the process; in the ... (Stochastic processes) [100%] 2024-01-02 [Stochastic processes]
4. Quantum stochastic processes: Quantum theory emerged as a new mechanics, but it was soon realized that it was also a new probability theory. The difference between classical and quantum probability is usually taken to be the fact that in the former probabilities of ... (Mathematics) [100%] 2023-10-06
5. Law (stochastic processes): In mathematics, the law of a stochastic process is the measure that the process induces on the collection of functions from the index set into the state space. The law encodes a lot of information about the process; in the ... (Stochastic processes) [100%] 2023-12-16 [Stochastic processes]
6. Smoothing problem (stochastic processes): The smoothing problem (not to be confused with smoothing in statistics, image processing and other contexts) is the problem of estimating an unknown probability density function recursively over time using incremental incoming measurements. It is one of the main problems ... (Stochastic processes) [86%] 2023-12-17 [Bayesian estimation] [Nonlinear filters]...
7. Stochastic processes, filtering of: filtration of stochastic processes The problem of estimating the value of a stochastic process $ Z ( t) $ at the current moment $ t $ given the past of another stochastic process related to it. For example, estimate a stationary process $ Z ( t) $ given ... (Mathematics) [86%] 2023-11-15
8. Infinitesimal generator (stochastic processes): In mathematics — specifically, in stochastic analysis — the infinitesimal generator of a Feller process (i.e. a continuous-time Markov process satisfying certain regularity conditions) is a Fourier multiplier operator that encodes a great deal of information about the process. (Stochastic processes) [86%] 2023-12-29 [Stochastic differential equations]
9. Stochastic processes, prediction of: extrapolation of stochastic processes The problem of estimating the values of a stochastic process $ X ( t) $ in the future $ t > s $ from its observed values up to the current moment of time $ s $. Usually one has in mind the extrapolation ... (Mathematics) [86%] 2023-10-21
10. Stochastic processes, interpolation of: The problem of estimating the values of a stochastic process $ X ( t) $ on some interval $ a < t < b $ using its observed values outside this interval. Usually one has in mind the interpolation estimator $ \widehat{X} ( t) $ for which the mean ... (Mathematics) [86%] 2023-09-11
11. Filtering problem (stochastic processes): In the theory of stochastic processes, filtering describes the problem of determining the state of a system from an incomplete and potentially noisy set of observations. While originally motivated by problems in engineering, filtering found applications in many fields from ... (Stochastic processes) [86%] 2024-06-12 [Control theory] [Signal estimation]...
12. Infinitesimal generator (stochastic processes): In mathematics — specifically, in stochastic analysis — the infinitesimal generator of a Feller process (i.e. a continuous-time Markov process satisfying certain regularity conditions) is a Fourier multiplier operator that encodes a great deal of information about the process. (Stochastic processes) [86%] 2025-01-30 [Stochastic differential equations]
13. List of stochastic processes topics: In the mathematics of probability, a stochastic process is a random function. In practical applications, the domain over which the function is defined is a time interval (time series) or a region of space (random field). (None) [77%] 2023-02-17 [Mathematics-related lists] [Stochastic processes]...
14. Statistical problems in the theory of stochastic processes: A branch of mathematical statistics devoted to statistical inferences on the basis of observations represented as a random process. In the most common formulation, the values of a random function $ x( t) $ for $ t \in T $ are observed, and on ... (Mathematics) [61%] 2023-10-13