Interconnection between Wick multiplication and integration on spaces of nonregular generalized functions in the Lévy white noise analysis
Анотація
We deal with spaces of nonregular generalized functions in the Lévy white noise analysis, which are constructed using Lytvynov's generalization of a chaotic representation property. Our aim is to describe a relationship between Wick multiplication and integration on these spaces. More exactly, we show that when employing the Wick multiplication, it is possible to take a time-independent multiplier out of the sign of an extended stochastic integral; establish an analog of this result for a Pettis integral (a weak integral); and prove a theorem about a representation of the extended stochastic integral via the Pettis integral from the Wick product of the original integrand by a Lévy white noise. As examples of an application of our results, we consider some stochastic equations with Wick type nonlinearities.
Класифікація
Ідентифікатори
Рецензії (0)
Написати рецензіюРецензій ще немає. Будьте першим!
Схожі роботи
Transformations of Wiener measure and orthogonal expansions
Схоже за: Mathematical and Theoretical Analysis · Stochastic processes and financial applications
Exponential formula and Girsanov theorem for mixed semilinear stochastic differential equations.
Схоже за: Mathematical and Theoretical Analysis · Stochastic processes and financial applications
Maximum Likelihood Drift Estimation for the Mixing of Two Fractional Brownian Motions
Схоже за: Stochastic processes and financial applications · Complex Systems and Time Series Analysis
Approximation of multifractional Brownian motion by absolutely continuous processes
Схоже за: Stochastic processes and financial applications · Complex Systems and Time Series Analysis
Stochastic differential equations driven by a Wiener process and fractional Brownian motion: Convergence in Besov space with respect to a parameter
Схоже за: Stochastic processes and financial applications · Complex Systems and Time Series Analysis
Dynamics of 1D discontinuous maps with multiple partitions and linear functions having the same fixed point. An application to financial market modeling
Схоже за: Stochastic processes and financial applications · Complex Systems and Time Series Analysis