An L p -theory for diffusion equations related to stochastic processes with non-stationary independent increment

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Abstract

Let X =(X t ) t≥0 be a stochastic process which has a (not necessarily stationary) independent increment on a probability space (Ω, P). In this paper, we study the following Cauchy problem related to the stochastic process X: (Formula presented) We provide a sufficient condition on X (see Assumptions 2.1 and 2.2) to guarantee the unique solvability of equation (*) in L p ([0,T]; H p φ ), where H p φ is a φ-potential space on R d (see Definition 2.9). Furthermore we show that for this solution, (Formula presented), where N is independent of u and f.

Original languageEnglish
Pages (from-to)3417-3450
Number of pages34
JournalTransactions of the American Mathematical Society
Volume371
Issue number5
DOIs
Publication statusPublished - 2019 May 1

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Keywords

  • Diffusion equation for jump process
  • L -theory
  • Non-stationary increment
  • Pseudo-differential operator

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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