In this article, we study the high resolution quantization problem for Rdvalued stochastic processes X that are solutions of stochastic differential equations. We let C([0, 1],Rd) denote the set of continuous functions mapping [0, 1] to Rd and denote by ‖·‖[0,1] the corresponding supremum norm, i.e. ‖f‖[0,1] = supt∈[0,1] |f(t)|. Analogously, Lq([0, 1],Rd) denotes the Lq-space of functions mappi...

We study the small time path behavior of double stochastic integrals of the form ∫ t 0 ( ∫ r 0 b(u)dW (u)) dW (r), where W is a d-dimensional Brownian motion and b an integrable progressively measurable stochastic process taking values in the set of d× dmatrices. We prove a law of the iterated logarithm that holds for all bounded progressively measurable b and give additional results under cont...

Summarizing the 20-year's experience of surgical treatment of ulcerative colitis and Crohn’s disease, we came to conclusion that this pathology occurs among young people in most cases. The disease often develops with different intestinal and extraintestinal complications and the pathological process in short terms covers the entire colon. In this connection it is necessary to carry out extensiv...

The concept of quasi-continuity and the new concept of almost compactness for a function are the basis for the extension of the contraction principle in large devi­ ations presented here. Important equivalences for quasi-continuity are proved in the case of metric spaces. The relation between the exponential tightness of a sequence of stochastic processes and the exponential tightness of its tr...

We introduce and study very general stochastic positive linear operators induced by general positive linear operators that are acting on continuous functions. These are acting on the space of real differentiable stochastic processes. Under some very mild, general and natural assumptions on the stochastic processes we produce related stochastic Shisha–Mond type inequalities of L-type 1 ≤ q < ∞ a...

We define the Burgers superprocess to be the solution of the stochastic partial differential equation ∂ ∂t u(t, x) =∆u(t, x) − λu(t, x)∇u(t, x) + γ √ u(t, x) W (dt, dx), where t ≥ 0, x ∈ R, and W is space-time white noise. Taking γ = 0 gives the classic Burgers equation, an important, non-linear, partial differential equation. Taking λ = 0 gives the super Brownian motion, an important, measure ...

This paper concerns the modelling of stochastic processes by means of dynamic factor models. In such models the observed process is decomposed into a structured part called the latent process, and a remainder that is called noise. The observed variables are treated in a symmetric way, so that no distinction between inputs and outputs is required. This motivates the condition that also the prior...