Perpetual integral functionals of multidimensional stochastic processes

Kondratiev Y, Mishura Y, da Silva JL (2021)
Stochastics : An International Journal of Probability and Stochastic Processes .

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Autor*in
Kondratiev, YuriUniBi; Mishura, Yuliya; da Silva, Jose L.
Abstract / Bemerkung
The paper is devoted to the existence of perpetual integral functionals integral(infinity)(0)f(X(t)) dt for 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 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 not equal 0.
Stichworte
Perpetual integral functionals; multidimensional processes; Brownian; motion; compound Poisson process; Markov process; fractional Brownian; motion
Erscheinungsjahr
2021
Zeitschriftentitel
Stochastics : An International Journal of Probability and Stochastic Processes
ISSN
1744-2508
eISSN
1744-2516
Page URI
https://pub.uni-bielefeld.de/record/2953395

Zitieren

Kondratiev Y, Mishura Y, da Silva JL. Perpetual integral functionals of multidimensional stochastic processes. Stochastics : An International Journal of Probability and Stochastic Processes . 2021.
Kondratiev, Y., Mishura, Y., & da Silva, J. L. (2021). Perpetual integral functionals of multidimensional stochastic processes. Stochastics : An International Journal of Probability and Stochastic Processes . https://doi.org/10.1080/17442508.2021.1900185
Kondratiev, Y., Mishura, Y., and da Silva, J. L. (2021). Perpetual integral functionals of multidimensional stochastic processes. Stochastics : An International Journal of Probability and Stochastic Processes .
Kondratiev, Y., Mishura, Y., & da Silva, J.L., 2021. Perpetual integral functionals of multidimensional stochastic processes. Stochastics : An International Journal of Probability and Stochastic Processes .
Y. Kondratiev, Y. Mishura, and J.L. da Silva, “Perpetual integral functionals of multidimensional stochastic processes”, Stochastics : An International Journal of Probability and Stochastic Processes , 2021.
Kondratiev, Y., Mishura, Y., da Silva, J.L.: Perpetual integral functionals of multidimensional stochastic processes. Stochastics : An International Journal of Probability and Stochastic Processes . (2021).
Kondratiev, Yuri, Mishura, Yuliya, and da Silva, Jose L. “Perpetual integral functionals of multidimensional stochastic processes”. Stochastics : An International Journal of Probability and Stochastic Processes (2021).

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