Kalman filter with variance components
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...
Kendall's identity for the first crossing time revisited.
Kingman's subadditive ergodic theorem
Kolmogorov equation and large-time behaviour for fractional Brownian motion driven linear SDE's
We consider a stochastic process which solves an equation where and are real matrices and is a fractional Brownian motion with Hurst parameter . The Kolmogorov backward equation for the function is derived and exponential convergence of probability distributions of solutions to the limit measure is established.
KPZ formula for log-infinitely divisible multifractal random measures
We consider the continuous model of log-infinitely divisible multifractal random measures (MRM) introduced in [E. Bacry et al. Comm. Math. Phys. 236 (2003) 449–475]. If M is a non degenerate multifractal measure with associated metric ρ(x,y) = M([x,y]) and structure function ζ, we show that we have the following relation between the (Euclidian) Hausdorff dimension dimH of a measurable set K and the Hausdorff dimension dimHρ with respect to ρ of the same set: ζ(dimHρ(K)) = dimH(K). Our results can...
KPZ formula for log-infinitely divisible multifractal random measures
We consider the continuous model of log-infinitely divisible multifractal random measures (MRM) introduced in [E. Bacry et al. Comm. Math. Phys.236 (2003) 449–475]. If M is a non degenerate multifractal measure with associated metric ρ(x,y) = M([x,y]) and structure function ζ, we show that we have the following relation between the (Euclidian) Hausdorff dimension dimH of a measurable set K and the Hausdorff dimension dimHρ with respect to ρ of the same set: ζ(dimHρ(K)) = dimH(K). Our results can...
Krickeberg's decomposition for local martingales
Krovkin Systems of Stochastic Processes.
inequalities for functionals of brownian motion
L1 Norm of Lévy Processes with Exponential Tails.
La chaîne de Feller et les chaînes associées
La classe des semimartingales qui permettent d'intégrer les processus optionnels
La convergence en loi pour les processus à valeurs dans un espace nucléaire
La entropía no aditiva de orden α y tipo β de un proceso puntual.
En esta comunicación se establece una medida de la entropía contenida en un proceso puntual mediante el concepto de entropía de orden α y tipo β introducida por Sharma and Mittal (1975); quedando, de este modo, generalizada la entropía de McFadden. Una vez que se estudian las propiedades relativas a la tasa de cambio de la Entropía, se demuestra que el proceso de Poisson es el de Entropía máxima dentro de la clase de los procesos puntuales estacionarios.
La loi des grands nombres pour une suite échangeable
La loi du logarithme itéré bornée dans les espaces de Banach
La loi du logarithme itéré pour les variables aléatoires prégaussiennes à valeurs dans un espace de Banach à norme régulière
La loi forte des grands nombres pour les processus harmonisables
La mesure de H. Föllmer en théorie des surmartingales