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Citations since 2017
6 Research Items
The Cauchy problem for the wave equation on the line driven by a general stochastic measure is studied. The existence, uniqueness, and Hölder regularity of the mild solution are proved. The continuous dependence of the solution on the data is established.
We study a stochastic parabolic differential equation generated by a general stochastic measure. The existence, uniqueness, and Hölder regularity of the mild solution are established.
Stochastic heat equation on [0, T] × ℝd, d ≥ 1, driven by a general stochastic measure µ(t), t ∊ [0, T], is studied in this paper. The existence, uniqueness, and Hölder regularity of a mild solution are proved.
For general stochastic measures, we assume only sigma-addivivity in probability on sigma-algebra. Equations with such stochastic integrator are studied.