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  2. Reflection principle (Wiener process) - Wikipedia

    en.wikipedia.org/wiki/Reflection_principle...

    More formally, the reflection principle refers to a lemma concerning the distribution of the supremum of the Wiener process, or Brownian motion. The result relates the distribution of the supremum of Brownian motion up to time t to the distribution of the process at time t. It is a corollary of the strong Markov property of Brownian motion.

  3. Appell's equation of motion - Wikipedia

    en.wikipedia.org/wiki/Appell's_equation_of_motion

    In classical mechanics, Appell's equation of motion (aka the Gibbs–Appell equation of motion) is an alternative general formulation of classical mechanics described by Josiah Willard Gibbs in 1879 [1] and Paul Émile Appell in 1900.

  4. Dynamical billiards - Wikipedia

    en.wikipedia.org/wiki/Dynamical_billiards

    The motion of the particle in the billiard is a straight line, with constant energy, between reflections with the boundary (a geodesic if the Riemannian metric of the billiard table is not flat). All reflections are specular: the angle of incidence just before the collision is equal to the angle of reflection just after the

  5. Reflected Brownian motion - Wikipedia

    en.wikipedia.org/wiki/Reflected_Brownian_motion

    A d–dimensional reflected Brownian motion Z is a stochastic process on + uniquely defined by a d–dimensional drift vector μ; a d×d non-singular covariance matrix Σ and; a d×d reflection matrix R. [8] where X(t) is an unconstrained Brownian motion with drift μ and variance Σ, and [9]

  6. Itô diffusion - Wikipedia

    en.wikipedia.org/wiki/Itô_diffusion

    This Wiener process (Brownian motion) in three-dimensional space (one sample path shown) is an example of an Itô diffusion.. A (time-homogeneous) Itô diffusion in n-dimensional Euclidean space is a process X : [0, +∞) × Ω → R n defined on a probability space (Ω, Σ, P) and satisfying a stochastic differential equation of the form

  7. Rotation formalisms in three dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotation_formalisms_in...

    Rotation formalisms are focused on proper (orientation-preserving) motions of the Euclidean space with one fixed point, that a rotation refers to.Although physical motions with a fixed point are an important case (such as ones described in the center-of-mass frame, or motions of a joint), this approach creates a knowledge about all motions.

  8. Motion (geometry) - Wikipedia

    en.wikipedia.org/wiki/Motion_(geometry)

    A glide reflection is a type of Euclidean motion.. In geometry, a motion is an isometry of a metric space.For instance, a plane equipped with the Euclidean distance metric is a metric space in which a mapping associating congruent figures is a motion. [1]

  9. Rigid transformation - Wikipedia

    en.wikipedia.org/wiki/Rigid_transformation

    (A reflection would not preserve handedness; for instance, it would transform a left hand into a right hand.) To avoid ambiguity, a transformation that preserves handedness is known as a rigid motion, a Euclidean motion, or a proper rigid transformation. In dimension two, a rigid motion is either a translation or a rotation.