Kac functional and Schrödinger equation
Kac’s chaos and Kac’s program
In this note I present the main results about the quantitative and qualitative propagation of chaos for the Boltzmann-Kac system obtained in collaboration with C. Mouhot in [33] which gives a possible answer to some questions formulated by Kac in [25]. We also present some related recent results about Kac’s chaos and Kac’s program obtained in [34, 23, 13] by K. Carrapatoso, M. Hauray, C. Mouhot, B. Wennberg and myself.
Karamata's Iteration Theorem And Normed Regularly Varying Sequences In A Historical Light
Karhunen-Loève expansions of α-Wiener bridges
We study Karhunen-Loève expansions of the process(X t(α))t∈[0,T) given by the stochastic differential equation , with the initial condition X 0(α) = 0, where α > 0, T ∈ (0, ∞), and (B t)t≥0 is a standard Wiener process. This process is called an α-Wiener bridge or a scaled Brownian bridge, and in the special case of α = 1 the usual Wiener bridge. We present weighted and unweighted Karhunen-Loève expansions of X (α). As applications, we calculate the Laplace transform and the distribution function...
Kategorientheoretische Behandlung der Zustandsraumtransformation von Markoffprozessen.
Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space II
This work is concerned with the existence and regularity of solutions to the Neumann problem associated with a Ornstein–Uhlenbeck operator on a bounded and smooth convex set K of a Hilbert space H. This problem is related to the reflection problem associated with a stochastic differential equation in K.