Perpetual integral functionals of multidimensional stochastic processes
Анотація
The paper is devoted to the existence of perpetual integral functionals ∫0∞f(X(t))dtfor several classes of d-dimensional of stochastic processes X(t). The method is very simple: we establish the conditions supplying that these functionals have a finite expectation. Examples of these classes include d-dimensional fractional Brownian motion having coordinates with the same Hurst index H, for which existence is established under the assumption d>1/H. In particular, perpetual integral functionals exist for d-dimensional Brownian motion with d>2, compound Poisson process, Markov processes admitting densities of transitional probabilities. In the case of Brownian motion and fractional Brownian motion we establish that the perpetual integral functionals are not a constant a.s. if f≠0.
Класифікація
Ідентифікатори
Рецензії (0)
Написати рецензіюРецензій ще немає. Будьте першим!
Схожі роботи
On a Brownian motion with a hard membrane
Схоже за: Stochastic processes and financial applications · advanced mathematical theories · Stochastic processes and statistical mechanics
Properties of Gaussian local times
Схоже за: Stochastic processes and financial applications · advanced mathematical theories · Stochastic processes and statistical mechanics
Averaging principle for the heat equation driven by a general stochastic measure
Схоже за: Stochastic processes and financial applications · advanced mathematical theories · Stochastic processes and statistical mechanics
Pseudodifferential Equation of Fluctuations of Nonstationary Gravitational Fields
Схоже за: Stochastic processes and financial applications · advanced mathematical theories · Stochastic processes and statistical mechanics
On recurrence and transience of some Lévy-type processes in ℝ
Схоже за: Stochastic processes and financial applications · advanced mathematical theories · Stochastic processes and statistical mechanics
Approximation of fractional Brownian motion by Wiener integrals
Схоже за: Stochastic processes and financial applications · advanced mathematical theories · Stochastic processes and statistical mechanics