Constructing stochastic flows of kernels

Georgii Riabov
Theory of Stochastic Processes
Vol.29 (45), no.1, 2025, pp.90-117
In the paper we suggest a new construction of stochastic flows of kernels in a locally compact separable metric space M. Starting from a consistent sequence of Feller transtition function (P⁽ⁿ⁾: n ≥ 1) on M we prove existence of a stochastic flow of kernels K=(K_s,t: -∞ < s ≤ t < ∞) in M, such that distributions of n-point motions of K are determined by P⁽ⁿ⁾. Presented construction allows to find a single idempotent measurable presentation 𝔭 of distributions of all kernels K_s,t from a flow, and to construct a flow that is invariant under 𝔭 and is jointly measurable in all arguments.
DOI: https://doi.org/10.3842/tsp-4382263085-56
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