Sample Paths Properties of Stochastic Processes from Orlicz Spaces, with Applications to Partial Differential Equations

  • Lyudmyla Sakhno Taras Shevchenko National University of Kyiv
  • Yuriy Kozachenko
  • Enzo Orsingher
  • Olha Hopkalo
Keywords: stochastic processes from Orlicz spaces, distribution of supremum, continuity, boundedness, entropy methods, partial differential equations, random initial conditions


In the present paper we obtain conditions for stochastic processes from Orlicz spaces to have almost sure bounded and continuous sample paths, the study is concerned with the processes defined on unbounded domains. Estimates for the distributions of suprema of the processes are also presented. Conditions are given in terms of entropy integrals and majorant characteristics of Orlicz spaces. Possible applications to solutions of partial differential equations are discussed. Examples of processes are given for which conditions of the main results are satisfied.


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How to Cite
Sakhno, L., Kozachenko, Y., Orsingher, E., & Hopkalo, O. (2020). Sample Paths Properties of Stochastic Processes from Orlicz Spaces, with Applications to Partial Differential Equations. Statistics, Optimization & Information Computing, 8(3), 722-739.
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