M. V. Platonova, “On a probabilistic approach to the Cauchy problem solution for an evolution equation with a higher even-order differential operator and a variable coefficient”, Zap. Nauchn. Sem. POMI, 2025, Volume 544,Pages <nobr>262

On a probabilistic approach to the Cauchy problem solution for an evolution equation with a higher even-order differential operator and a variable coefficient

M. V. Platonova^ab

^a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
^b Chebyshev Laboratory, St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: We construct a probabilistic approximation of the solution to the Cauchy problem for an evolution equation containing a higher even-order differential operator with a variable coefficient on its right-hand side. The approximation is expressed as the mathematical expectation of functionals of a stochastic process.

Key words and phrases: evolution equation, Cauchy problem, limit theorem.

UDC: 519.2

Received: 12.10.2025