Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 3

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: Gaussian field

Sortuj według:

Ogranicz wyniki do:

Finitely additive functions in measure theory and applications

Alpay Daniel, Jorgensen Palle

Opuscula Mathematica

2024

Vol. 44, no. 3

323--339

In this paper, we consider, and make precise, a certain extension of the Radon–Nikodym derivative operator, to functions which are additive, but not necessarily sigma-additive, on a subset of a given sigma-algebra. We give applications to probability theory; in particular, to the study of μ-Brownian motion, to stochastic calculus via generalized Itô-integrals, and their adjoints (in the form of generalized stochastic derivatives), to systems of transition probability operators indexed by families of measures μ, and to adjoints of composition operators.

Optimal importance sampling for continuous Gaussian fields

Pacchiarotti Barbara

Journal of Applied Analysis

2020

Vol. 26, nr 2

161--171

We consider the problem of selecting a change of mean which minimizes the variance of Monte Carlo estimators for the expectation of a functional of a continuous Gaussian field, in particular continuous Gaussian processes. Functionals of Gaussian fields have taken up an important position in many fields including statistical physics of disordered systems and mathematical finance (see, for example, [A. Comtet, C.Monthus and M. Yor, Exponential functionals of Brownian motion and disordered systems, J. Appl. Probab. 35 (1998), no. 2, 255-271], [D. Dufresne, The integral of geometric Brownian motion, Adv. in Appl. Probab. 33 (2001), no. 1, 223-241], [N. Privault and W. I. Uy, Monte Carlo computation of the Laplace transform of exponential Brownian functionals, Methodol. Comput. Appl. Probab. 15 (2013), no. 3, 511-524] and [V. R. Fatalov, On the Laplace method for Gaussian measures in a Banach space, Theory Probab. Appl. 58 (2014), no. 2, 216-241]. Naturally, the problem of computing the expectation of such functionals, for example the Laplace transform, is an important issue in such fields. Some examples are considered, which, for particular Gaussian processes, can be related to option pricing.

Central limit theorem for a Gaussian incompressible flow with additional Brownian noise

Miernowski T.

Probability and Mathematical Statistics

2003

Vol. 23, Fasc. 2

413--434

We generalize the result of Komorowski and Papanicolaou published in [7]. We consider the solution of stochastic differential equation dX (t) = V (t, X(t)) dt + √2κdB(t), where B(t) is a standard d-dimensional Brownian motion and V (t, x), (t, x) ∈ R × Rd, is a d-dimensional, incompressible, stationary, random Gaussian field decorrelating in finite time. We prove that the weak limit as ε ↓ 0 of the family of rescaled processes Xε(t) = εX(t/ε2) exists and may be identified as a certain Brownian motion.