Kolmogorov's continuity theorem
GPTKB entity
Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:theorem
|
| gptkbp:appliesTo |
stochastic processes
|
| gptkbp:claims |
existence of continuous modifications of stochastic processes
|
| gptkbp:has_implications_for |
continuity of sample paths
|
| https://www.w3.org/2000/01/rdf-schema#label |
Kolmogorov's continuity theorem
|
| gptkbp:is_a |
random variables
|
| gptkbp:is_a_platform_for |
theory of stochastic processes
the study of stochastic differential equations |
| gptkbp:is_a_subject_of |
probability theory
measure theory the theory of random walks has applications in various fields provides a framework for continuity in stochastic processes addresses continuity in probability ensures the existence of continuous paths has implications for statistical inference is widely cited in research papers provides continuity conditions the study of random processes. |
| gptkbp:is_essential_for |
statistical mechanics
mathematical finance the study of diffusion processes the study of chaos theory the analysis of random fields the analysis of random phenomena the development of probabilistic models the study of random functions theory of martingales |
| gptkbp:is_part_of |
stochastic analysis
|
| gptkbp:is_recognized_for |
the existence of stochastic integrals
|
| gptkbp:is_referenced_in |
textbooks on probability
|
| gptkbp:is_used_in |
machine learning
data science signal processing probability theory financial mathematics pathwise_continuity |
| gptkbp:isConnectedTo |
Itô calculus
the central limit theorem |
| gptkbp:previousName |
gptkb:Andrey_Kolmogorov
|
| gptkbp:publishedBy |
1933
|
| gptkbp:related_to |
Brownian motion
Markov processes Gaussian processes the theory of ergodic processes the theory of stochastic control |
| gptkbp:suitableFor |
time series analysis
stochastic calculus quantum_mechanics |
| gptkbp:was_a_result_of |
functional analysis
continuity of stochastic processes |